Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients
From MaRDI portal
Publication:1578960
DOI10.1007/s002050000082zbMath0958.35060OpenAlexW2077024482MaRDI QIDQ1578960
Michael S. Vogelius, Yan-yan Li
Publication date: 27 March 2001
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002050000082
PDEs with low regular coefficients and/or low regular data (35R05) Elliptic equations and elliptic systems (35J99) Perturbations of PDEs on manifolds; asymptotics (58J37)
Related Items
Gradient estimates for the insulated conductivity problem: The case of m-convex inclusions, Gradient estimates in generalized Morrey spaces for parabolic operators, W1,q REGULARITY RESULTS FOR ELLIPTIC TRANSMISSION PROBLEMS ON HETEROGENEOUS POLYHEDRA, Singularities of the stress concentration in the presence of 𝐶^{1,𝛼}-inclusions with core-shell geometry, Singular Behavior of Electric Field of High-Contrast Concentrated Composites, Estimates for elliptic systems in a narrow region arising from composite materials, Derivative estimates of solutions of elliptic systems in narrow regions, Gradient Estimates for Stokes and Navier--Stokes Systems with Piecewise DMO Coefficients, Upper and lower bounds for stress concentration in linear elasticity when 𝐶^{1,𝛼} inclusions are close to boundary, Gradient Estimates for Electric Fields with MultiScale Inclusions in the Quasi-Static Regime, Two types of electric field enhancements by infinitely many circular conductors arranged closely in two parallel lines, Optimal estimates for the conductivity problem close to the boundary in dimension greater than two, Optimal Estimates for the Perfect Conductivity Problem with Inclusions Close to the Boundary, Fully nonlinear free transmission problems, Eigenfunctions Localised on a Defect in High-Contrast Random Media, Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer, \(W^{1,p}\) estimates for nonlinear Schrödinger equations with partially BMO coefficients in Reifenberg domains, Optimal estimates for transmission problems including relative conductivities with different signs, The perfect conductivity problem with arbitrary vanishing orders and non-trivial topology, BMO-regularity for a degenerate transmission problem, Stochastic Homogenization and Geometric Singularities: A Study on Corners, Regularity of viscosity solutions to fully nonlinear elliptic transmission problems, Gradient estimates for the insulated conductivity problem with inclusions of the general m‐convex shapes, Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited, Quantitative nonlinear homogenization: control of oscillations, The Dielectric Boundary Force in Molecular Solvation of the Generalized Poisson–Boltzmann Equation with Ionic Sizes, A high order discontinuous Galerkin method for the recovery of the conductivity in electrical impedance tomography, Analysis of nonlinear poroviscoelastic flows with discontinuous porosities *, Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow, Calderón‐Zygmund estimates for higher order elliptic equations from composite material, Stress blow-up analysis when suspending rigid particles approach boundary in 3D Stokes flow, Quantitative analysis of field concentration in presence of closely located inclusions of high contrast, Enhanced Electrical Impedance Tomographyviathe Mumford–Shah Functional, Stable determination of an inclusion for a class of anisotropic conductivities, Unnamed Item, Asymptotics for the Electric Field Concentration in the Perfect Conductivity Problem, Quantitative Homogenization for the Case of an Interface Between Two Heterogeneous Media, ASYMPTOTIC EXPANSIONS FOR HIGH-CONTRAST ELLIPTIC EQUATIONS, Mach configuration in pseudo-stationary compressible flow, Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements, Estimates for the electric field in the presence of adjacent perfectly conducting spheres, Unnamed Item, On the Convergence Rates of GMsFEMs for Heterogeneous Elliptic Problems Without Oversampling Techniques, Asymptotics of the Gradient of Solutions to the Perfect Conductivity Problem, A New Optimization Approach to Sparse Reconstruction of Log-Conductivity in Acousto-Electric Tomography, Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions, Some quantitative homogenization results in a simple case of interface, Gradient Estimates for Divergence Form Elliptic Systems Arising from Composite Material, Unnamed Item, Approximate transmission conditions through a rough thin layer: The case of periodic roughness, Asymptotic expansions for the voltage potentials with two-dimensional and three-dimensional thin interfaces, Blow-up of Electric Fields between Closely Spaced Spherical Perfect Conductors, A sharp regularity result of solutions of a transmission problem, Global Regularity and Multiscale Approach for Thermal Radiation Heat Transfer, Unification of the Probe and Singular Sources Methods for the Inverse Boundary Value Problem by the No-Response Test, Large-scale Lipschitz estimates for elliptic systems with periodic high-contrast coefficients, Multiscale Analysis and Computation for a Stationary Schrödinger--Poisson System in Heterogeneous Nanostructures, Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional, Optimal Sobolev Regularity for Linear Second-Order Divergence Elliptic Operators Occurring in Real-World Problems, Multiscale Computation and Convergence for Coupled Thermoelastic System in Composite Materials, Subsonic Flows Past a Profile with a Vortex Line at the Trailing Edge, An optimal estimate for electric fields on the shortest line segment between two spherical insulators in three dimensions, \(L^{p}\) gradient estimate for elliptic equations with high-contrast conductivities in \(\mathbb{R}^n\), Asymptotic analysis for the electric field concentration with geometry of the core-shell structure, Gradient estimates for divergence form parabolic systems from composite materials, Gradient estimates for the perfect conductivity problem, Global gradient estimates for nonlinear equations of \(p\)-Laplace type from composite materials, On an elliptic equation arising from composite materials, Asymptotic analysis of second-order boundary layer correctors, Quantitative stability estimates for a two-phase Serrin-type overdetermined problem, Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains, Anisotropic conductivity problem with both perfect and insulated inclusions, Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate, Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of \(p\)-growth, Gradient estimates for solutions of the Lamé system with partially infinite coefficients in dimensions greater than two, Sharp regularity for elliptic systems associated with transmission problems, Uniform bound and convergence for elliptic homogenization problems, Stability of contact discontinuity for steady Euler system in infinite duct, Gradient estimates for elliptic systems from composite materials with closely spaced stiff \(C^{1, \gamma}\) inclusions, Boundary-contact problems for domains with edge singularities, Hessian estimates for non-divergence form elliptic equations arising from composite materials, Interior Hölder and gradient estimates for the homogenization of the linear elliptic equations, Lower bounds of gradient's blow-up for the Lamé system with partially infinite coefficients, Regularity for \(C^{1, \alpha}\) interface transmission problems, Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching \(C^{1, \gamma }\)-inclusions, Regularity of \(\mathcal C^1\) and Lipschitz domains in terms of the Beurling transform, On the spectrum of the Poincaré variational problem for two close-to-touching inclusions in 2D, Optimal estimates and asymptotics for the stress concentration between closely located stiff inclusions, Asymptotics of the solution to the conductivity equation in the presence of adjacent circular inclusions with finite conductivities, On the robustness of multiscale hybrid-mixed methods, Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation, Hölder estimate for non-uniform parabolic equations in highly heterogeneous media, A multiscale parallel algorithm for dual-phase-lagging heat conduction equation in composite materials, A priori estimate for non-uniform elliptic equations, Elliptic equations with measurable nonlinearities in nonsmooth domains, Strong influence of a small fiber on shear stress in fiber-reinforced composites, Interior regularity estimates in high conductivity homogenization and application, Averaging of dilute random media: a rigorous proof of the Clausius-Mossotti formula, Spectral analysis of the Neumann-Poincaré operator and characterization of the stress concentration in anti-plane elasticity, Smoothness of the Beurling transform in Lipschitz domains, Differentiability of the Dirichlet to Neumann Map Under Movements of Polygonal Inclusions with an Application to Shape Optimization, Convergence for elliptic equations in periodic perforated domains, Gradient estimates of solutions to the insulated conductivity problem in dimension greater than two, The insulated conductivity problem, effective gradient estimates and the maximum principle, Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis., Effective boundary conditions arising from the heat equation with three-dimensional interior inclusion, Optimal estimates for the conductivity problem by Green's function method, Quantitative Jacobian determinant bounds for the conductivity equation in high contrast composite media, Explicit estimates for solutions of mixed elliptic problems, Multiscale asymptotic analysis and parallel algorithm of parabolic equation in composite materials, Lipschitz estimates and existence of correctors for nonlinearly elastic, periodic composites subject to small strains, Crack initiation in brittle materials, About solutions of Poisson's equation with transition condition in non-smooth domains, Stress concentration for closely located inclusions in nonlinear perfect conductivity problems, A multiscale algorithm for radiative heat transfer equation with rapidly oscillating coefficients, On a counter-example to quantitative Jacobian bounds, Optimal estimates for the electric field in two dimensions, Elliptic and parabolic equations in fractured media, Electric field concentration in the presence of an inclusion with eccentric core-shell geometry, Regularity of a transmission problem and periodic homogenization, \( W^{1,p}\) estimates for elliptic systems on composite material with almost partially BMO coefficients, The calculus of boundary variations and the dielectric boundary force in the Poisson-Boltzmann theory for molecular solvation, Interface dynamics in a two-phase tumor growth model, Gradient estimates for elliptic equations with measurable nonlinearities, Enhancement of elasto-dielectrics by homogenization of active charges, Asymptotics for the concentrated field between closely located hard inclusions in all dimensions, Global gradient estimates for parabolic systems from composite materials, Regularity in oscillatory nonlinear elliptic systems, Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities, Shape reconstruction of nanoparticles from their associated plasmonic resonances, Effective boundary conditions resulting from anisotropic and optimally aligned coatings: the two dimensional case, Gradient estimates for solutions of the Lamé system with partially infinite coefficients, Optimal elliptic Sobolev regularity near three-dimensional multi-material Neumann vertices, Direct computation of elliptic singularities across anisotropic, multi-material edges, Global existence and stability of a stationary Mach reflection, Elliptic equations with singular BMO coefficients in Reifenberg domains, Estimates and asymptotics for the stress concentration between closely spaced stiff \(C^{1, \gamma }\) inclusions in linear elasticity, Reconstruction of a penetrable obstacle by complex spherical waves, Gradient estimates for solutions to the conductivity problem, Gradient estimates for parabolic and elliptic systems from linear laminates, Global gradient estimates in weighted Lebesgue spaces for parabolic operators, Optimal gradient estimates for the perfect conductivity problem with \(C^{1,\alpha}\) inclusions, Gradient estimates for parabolic systems from composite material, Stable determination of an inhomogeneous inclusion by local boundary measurements, The asymptotics for the perfect conductivity problem with stiff \(C^{1,\alpha}\)-inclusions, Optimal bound on high stresses occurring between stiff fibers with arbitrary shaped cross-sections, Properties of mean value sets: angle conditions, blowup solutions, and nonconvexity, Extra cancellation of even Calderón-Zygmund operators and quasiconformal mappings, Gradient estimates for the perfect conductivity problem in anisotropic media, Characterization of electric fields between two spherical perfect conductors with general radii in 3D, Decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions, Global gradient estimate for a divergence problem and its application to the homogenization of a magnetic suspension, Lipschitz stability for the inverse conductivity problem, Boundary-contact problems for domains with conical singularities, Free transmission problems, Non-uniform elliptic equations in convex Lipschitz domains, Reifenberg flatness of free boundaries in obstacle problems with VMO ingredients, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. II: The full Maxwell equations., Recovering memory kernels in parabolic transmission problems in infinite time intervals: the non-accessible case, Existence of solutions to a fully nonlinear free transmission problem, Optimal boundary gradient estimates for Lamé systems with partially infinite coefficients