Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
scientific article; zbMATH DE number 3554969 - MaRDI portal

scientific article; zbMATH DE number 3554969

From MaRDI portal
Publication:4129368

zbMath0356.49008MaRDI QIDQ4129368

Luciano Modica, Stefano Mortola

Publication date: 1977


Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.



Related Items

Large data limit for a phase transition model with the p-Laplacian on point cloudsA consistent approximation of the total perimeter functional for topology optimization algorithmsAnalysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpaintingMultiple Delaunay ends solutions of the Cahn-Hilliard equationUnnamed ItemA Diffuse Interface Model for Cell Blebbing Including Membrane-Cortex Coupling with Linker DynamicsTopology optimization for quasistatic elastoplasticityA multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewettingGaussian Approximations for Transition Paths in Brownian DynamicsTruncated nonsmooth Newton multigrid for phase-field brittle-fracture problems, with analysisClassification and image processing with a semi‐discrete scheme for fidelity forced Allen–Cahn on graphsSharp interface limit of the Cahn–Hilliard reaction model for lithium-ion batteriesA relation of the Allen-Cahn equations and the Euler equations and applications of the equipartitionThe Yang-Mills-Higgs functional on complex line bundles: \(\Gamma\)-convergence and the London equationPhase separation on varying surfaces and convergence of diffuse interface approximationsHomogenization and phase separation with space dependent wells: the subcritical caseDiscrete Approximation of the Griffith Functional by Adaptive Finite ElementsApplications of PDEs inpainting to magnetic particle imaging and corneal topographyGeometric aspects of shape optimization“Gradient-free” diffuse approximations of the Willmore functional and Willmore flowTwo-Scale Elastic Shape Optimization for Additive ManufacturingMaterial optimization for nonlinearly elastic planar beamsInterfacial energy as a selection mechanism for minimizing gradient Young measures in a one-dimensional model problemVariational approximation of size-mass energies fork-dimensional currentsA gradient system with a wiggly energy and relaxed EDP-convergenceLocations of interior transition layers to inhomogeneous transition problems in higher -dimensional domainsJoint Reconstruction-Segmentation on GraphsAnalysis of a combined filtered/phase-field approach to topology optimization in elasticityMultiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifoldsMass concentration in rescaled first order integral functionalsOn the boundary regularity of phase-fields for Willmore's energyMean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere\(\Gamma\)-convergence and stochastic homogenisation of singularly-perturbed elliptic functionalsOn the Reconstruction of Cavities in a Nonlinear Model Arising from Cardiac ElectrophysiologyApproximation of multiphase mean curvature flows with arbitrary nonnegative mobilitiesEntire solutions to 4 dimensional Ginzburg-Landau equations and codimension 2 minimal submanifoldsConnections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image SegmentationSuper-resolution surface reconstruction from few low-resolution slicesΓ-convergence and stochastic homogenisation of phase-transition functionalsThe Alt–Phillips functional for negative powersConvergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functionalTwo-dimensional ferronematics, canonical harmonic maps and minimal connectionsMultiplicity‐1 minmax minimal hypersurfaces in manifolds with positive Ricci curvatureFractional elliptic problems on Lipschitz domains: regularity and approximationWeak solutions of Mullins-Sekerka flow as a Hilbert space gradient flowPartial differential equations from theory to applications: dedicated to Alberto Farina, on the occasion of his 50th birthdayUniform density estimates and \(\Gamma \)-convergence for the Alt-Phillips functional of negative powersGradient theory of domain walls in thin, nematic liquid crystals filmsSymmetry results for the solutions of a partial differential equation arising in water wavesA quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problemThe variational formulation of brittle fracture: numerical implementation and extensionsTopology Optimization for Incremental Elastoplasticity: A Phase-Field ApproachHigh Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard DynamicsMotion of a Droplet for the Stochastic Mass-Conserving Allen--Cahn EquationSecond-order \(\Gamma\)-limit for the Cahn-Hilliard functionalOne-dimensional solutions of non-local Allen-Cahn-type equations with rough kernelsMinimal surfaces and free boundaries: Recent developmentsAdaptive reconstruction for electrical impedance tomography with a piecewise constant conductivityPhase-field modelling and computing for a large number of phasesThree-Dimensional Volume Reconstruction Using Two-Dimensional Parallel SlicesAsymptotic behavior of the W1∕q,q-norm of mollified BV functions and applications to singular perturbation problemsOn material optimisation for nonlinearly elastic plates and shellsAn Analysis of Chevrons in Thin Liquid Crystal CellsPhase Field Methods for Binary RecoveryThe Hele–Shaw flow as the sharp interface limit of the Cahn–Hilliard equation with disparate mobilitiesTwo-Phase Segmentation for Intensity Inhomogeneous Images by the Allen--Cahn Local Binary Fitting ModelPhase-field methods for spectral shape and topology optimizationA sharp-interface limit for a two-well problem in geometrically linear elasticityDroplet solutions in the diblock copolymer problem with skewed monomer compositionOn the convergence of solutions of some evolution differential equationsA maximum principle for the system \(\Delta u- \nabla W(u)=0\)On De Giorgi's conjecture: recent progress and open problemsSimultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomographyMotion of concentration sets in Ginzburg-Landau equations.Critical points via \(\Gamma \)-convergence: general theory and applicationsSaddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)Gradient-flow techniques for the analysis of numerical schemes for multi-phase mean-curvature flowA metric-based approach to multiphase mean curvature flows with mobilitiesThe effect of a singular perturbation on nonconvex variational problemsGeometrically constrained wallsConvergence of the thresholding scheme for multi-phase mean-curvature flowTwo-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface modelComputationally efficient approach for the minimization of volume constrained vector-valued Ginzburg-Landau energy functionalLong-time behavior of a nonlocal Cahn-Hilliard equation with reactionOn a singular perturbation problem related to optimal lifting in BV-spaceMultimaterial topology optimization by volume constrained Allen-Cahn system and regularized projected steepest descent methodKinks in two-phase lipid bilayer membranesA Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditionsImage segmentation using some piecewise constant level set methods with MBO type of projectionGlobal dynamics of boundary dropletsA two-gradient approach for phase transitions in thin filmsDensity estimates for a variational model driven by the Gagliardo normRegularization of discrete contour by Willmore energyOn the \(\gamma\)-limit of singular perturbation problems with optimal profiles which are not one-dimensional. II: The lower bound\(\Gamma \)-convergence of variational functionals with boundary terms in Stein manifoldsA two scale \(\Gamma \)-convergence approach for random non-convex homogenizationA survey on the Blake-Zisserman functionalRegularity of the Eikonal equation with two vanishing entropiesA geometric Ginzburg-Landau problemA novel homogenization method for phase field approaches based on partial rank-one relaxationConvergence of phase-field free energy and boundary force for molecular solvationActuation of thin nematic elastomer sheets with controlled heterogeneityHomogenization of Cahn-Hilliard-type equations via evolutionary \(\Gamma\)-convergenceSingular perturbations of variational problems arising from a two-phase transition modelA new stochastic variational PDE model for soft Mumford-Shah segmentationVariational problems in SBV and image segmentationA zigzag pattern in micromagneticsSome properties of Gamma-limits of integral functionalsApproximation and relaxation of perimeter in the Wiener spaceAsymptotics for the fractional Allen-Cahn equation and stationary nonlocal minimal surfacesThe role of Gauss curvature in a membrane phase separation problemAsymptotic behavior of the Landau-Lifshitz model of ferromagnetismA fractal shape optimization problem in branched transportMinimal partitions and image classification using a gradient-free perimeter approximationOn De Giorgi's conjecture in dimension \(N\geq 9\)A Gamma-convergence approach to the Cahn-Hilliard equationA weighted gradient theory of phase transitions with a possibly singular and degenerate spatial inhomogeneitySecond order asymptotic development for the anisotropic Cahn-Hilliard functionalGamma limit of the nonself-dual Chern-Simons-Higgs energyOptimal profiles in a phase-transition model with a saturating fluxA phase-field approximation of the Steiner problem in dimension twoPhase-field approximations of the Willmore functional and flowNew asymptotic analysis method for phase field models in moving boundary problem with surface tensionIsogeometric analysis for topology optimization with a phase field modelLarge deviation principle for a stochastic Allen-Cahn equationSome results on surface measures in calculus of variationsClifford Tori and the singularly perturbed Cahn-Hilliard equationPeriodic solutions to a Cahn-Hilliard-Willmore equation in the planeA necessary condition for lower semicontinuity of line energiesNonlocal phase transitions in homogeneous and periodic media\(\Gamma\)-limits of singular perturbation problems involving energies with non-local termsUniqueness and stability of the saddle-shaped solution to the fractional Allen-Cahn equationPhase transitions with a minimal number of jumps in the singular limits of higher order theoriesAmbrosio-Tortorelli approximation of quasi-static evolution of brittle fracturesReconstruction of material losses by perimeter penalization and phase-field methodsSemilinear integro-differential equations. I. Odd solutions with respect to the Simons coneSoliton-stripe patterns of a functional with an attractive-repulsive-attractive interactionGraph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in imagesA one-dimensional variational problem for cholesteric liquid crystals with disparate elastic constantsRegional control for spatially structured mosquito borne epidemics. Malaria as a working exampleRegional control for spatially structured mosquito borne epidemics. II: Computational issuesChirality transitions in frustrated ferromagnetic spin chains: a link with the gradient theory of phase transitionsMultiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowiresDerivation of a linearised elasticity model from singularly perturbed multiwell energy functionalsA Modica-Mortola approximation for branched transportAsymptotic behaviour of time stepping methods for phase field modelsA fractional isoperimetric problem in the Wiener spaceA variational singular perturbation problem motivated by Ericksen's model for nematic liquid crystalsVariational approximation of interface energies and applicationsCompactness and sharp lower bound for a 2D smectics modelTravelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interactionPhase-field approximation of functionals defined on piecewise-rigid mapsSharp interface limit of a multi-phase transitions model under nonisothermal conditionsOne-dimensionality of the minimizers in the large volume limit for a diffuse interface attractive/repulsive model in general dimensionThe gradient theory of phase transitions and the minimal interface criterionThe quasistationary phase field equations with Neumann boundary conditionsNumerical experiments in revisited brittle fractureThe geometric structure of interfaces and free boundariesRigidity of a non-elliptic differential inclusion related to the Aviles-giga conjectureSecond order threshold dynamics schemes for two phase motion by mean curvatureExistence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluidsThe characterization of Riemannian metric arising from phase transition problemsCodimension one minimal cycles with coefficients in \(Z\) or \(Z_p\), and variational functionals on fibered spacesOn the variation of the fractional mean curvature under the effect of \(C^{1, \alpha}\) perturbationsReorientation of smectic a liquid crystals by magnetic fieldsContinuum limit of total variation on point cloudsSingular perturbation by bending for an adhesive obstacle problemLongest minimal length partitionsA rigorous sharp interface limit of a diffuse interface model related to tumor growthGeneration of tubular and membranous shape textures with curvature functionalsAnisotropic surface tensions for phase transitions in periodic mediaAsymptotic development by \(\Gamma{}\)-convergenceOn the total variation of the gradient of a functionNonconvex variational problems with anisotropic perturbationsHigher-order phase transitions with line-tension effectSingular Perturbation Problems Involving CurvatureFracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane caseA variational principle for pulsating standing waves and an Einstein relation in the sharp interface limitA counterexample to a conjecture by De Giorgi in large dimensionsA variational study of some hadron bag modelsOn global minimizers for a variational problem with long-range interactionsSecond-Order Edge-Penalization in the Ambrosio--Tortorelli functionalAsymptotic behavior of the interface for entire vector minimizers in phase transitionsA Variational Approach to the Inverse Photolithography ProblemOn the approximation of the elastica functional in radial symmetryMean curvature properties for \(p\)-Laplace phase transitionsRegularity of gradient vector fields giving rise to finite Caccioppoli partitionsVariational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar CaseDensity Estimates for Degenerate Double-Well PotentialsAnalysis of the Diffuse Domain Approach for a Bulk-Surface Coupled PDE SystemNumerical investigations of the role of curvature in strong segregation problems on a given surfaceSurface tension and \(\Gamma\)-convergence of Van der Waals-Cahn-Hilliard phase transitions in stationary ergodic mediaMinimal submanifolds from the abelian Higgs modelOn \(\Gamma\)-convergence of a variational model for Lithium-ion batteriesPartial differential equations and variational methods for geometric processing of imagesOptimal design of multiphase composites under elastodynamic loadingK-ended \(O(m) \times O(n)\) invariant solutions to the Allen-Cahn equation with infinite Morse indexConvergence rates for the Allen-Cahn equation with boundary contact energy: the non-perturbative regimeA two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flowA finer singular limit of a single-well Modica-Mortola functional and its applications to the Kobayashi-Warren-Carter energyWeak Lower Semicontinuity of Integral Functionals and ApplicationsSingular perturbations of variational problems of vector valued functionsOn the Łojasiewicz-Simon gradient inequality on submanifoldsExponentially slow motion of interface layers for the one-dimensional Allen-Cahn equation with nonlinear phase-dependent diffusivityNumerical minimization of a second-order functional for image segmentationOverhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energiesA posteriori error control for the binary Mumford-Shah modelCompactness estimates for minimizers of the Alt-Phillips functional of negative exponentsOn a conjecture of De Giorgi about the phase-field approximation of the Willmore functionalSymmetry and asymmetry of components for elliptic Gross-Pitaevskii systemLamellar phase solutions for diblock copolymers with nonlocal diffusionsDouble tori solution to an equation of mean curvature and Newtonian potentialA diffused interface with the advection term in a Sobolev spaceThe double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applicationsEquilibrium for multiphase solids with Eulerian interfacesLong-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn EquationQuantitative analysis of finite-difference approximations of free-discontinuity problemsA phase-field approach to variational hierarchical surface segmentationSharp Interface Limits for Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible FluidsNon-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditionsShape and topology optimizationCahn-Hilliard phase field theory coupled to mechanics: fundamentals, numerical implementation and application to topology optimizationAnisotropic free-discontinuity functionals as the Γ-limit of second-order elliptic functionalsApproximation of Partitions of Least Perimeter by Γ-Convergence: Around Kelvin’s ConjectureConvergence of phase-field approximations to the Gibbs-Thomson lawOn variational dimension reduction in structure mechanicsSymmetry in nonlinear PDEs: some open problemsFront propagation in geometric and phase field models of stratified mediaDeterministic equivalent for the Allen-Cahn energy of a scaling law in the Ising modelFinite element discretizations of nonlocal minimal graphs: ConvergenceUniform estimates for the parabolic Ginzburg–Landau equationVariational approximation of anisotropic functionals on partitionsTowards a counter-example to a conjecture of De Giorgi in high dimensionsDesign-dependent loads in topology optimizationLocal and Nonlocal Continuum Limits of Ising-Type Energies for Spin SystemsVolume Reconstruction from SlicesQualitative and Numerical Analysis of a Spectral Problem with Perimeter ConstraintThe \(\varGamma\)-limit of the two-dimensional Ohta-Kawasaki energy. I: Droplet densityOn stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\)Phase field approximations of branched transportation problemsDiffuse-Interface Approximations of Osmosis Free Boundary ProblemsTwo-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitionsSome energy estimates for stable solutions to fractional Allen-Cahn equationsSome basic facts on the system $\Delta u - W_{u} (u) = 0$Sharp Interface Limit for a Phase Field Model in Structural OptimizationPhase field approach to optimal packing problems and related Cheeger clustersRadial and cylindrical symmetry of solutions to the Cahn-Hilliard equationElastic curves and phase transitionsEfficient variational constitutive updates for Allen-Cahn-type phase field theory coupled to continuum mechanicsA phase-field approach to Eulerian interfacial energiesAsymptotic behavior of Allen-Cahn-type energies and Neumann eigenvalues via inner variationsWetting on rough surfaces and contact angle hysteresis: numerical experiments based on a phase field modelVariational approximation for detecting point-like target problemsUnnamed ItemInteraction between oscillations and singular perturbations in a one-dimensional phase-field modelGradient flows of non convex functionals in Hilbert spaces and applicationsLinear and nonlinear fractional elliptic problemsLearning phase field mean curvature flows with neural networksA new diffuse-interface approximation of the Willmore flowOne-dimensionality of the minimizers for a diffuse interface generalized antiferromagnetic model in general dimensionConvergence to equilibrium for time and space discretizations of the Cahn-Hilliard equationThreshold dynamics for the piecewise constant Mumford-Shah functionalAsymptotic analysis of second order nonlocal Cahn-Hilliard-type functionalsEntire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De GiorgiIntroduction: Big data and partial differential equationsFrustrated ferromagnetic spin chains: a variational approach to chirality transitions\(\Gamma\)-convergence approximation of fracture and cavitation in nonlinear elasticity