DOI10.1007/BF02921593zbMath0808.46046OpenAlexW2069241221MaRDI QIDQ1323554
David Kinderlehrer, Pablo Pedregal
Publication date: 30 June 1994
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02921593
Young measure solutions of a class of forward--backward diffusion equations ⋮
NUMERICAL SOLUTION OF A CLASS OF NON-CONVEX VARIATIONAL PROBLEMS BY SQP ⋮
Energy functionals depending on elastic strain and chemical composition ⋮
A class of singular diffusion equations based on the convex-nonconvex variation model for noise removal ⋮
Theory of functions of bounded variation and its applications ⋮
A sharp version of Zhang’s theorem on truncating sequences of gradients ⋮
Remarks on \(W^{1,p}\)-stability of the conformal set in higher dimensions. ⋮
A new approach to variational problems with multiple scales ⋮
A Quantization Property for Moving Line Vortices ⋮
Fine properties of functions of bounded deformation -- an approach via linear PDEs ⋮
On rank one convex functions that are homogeneous of degree one ⋮
On optimality conditions of relaxed non-convex variational problems ⋮
A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition ⋮
Existence of weak solutions for some quasilinear degenerated elliptic systems in weighted Sobolev spaces ⋮
Gradient Young Measures Generated by Quasi-Conformal Maps in the Plane ⋮
\(L^\infty\)-truncation of closed differential forms ⋮
Young measure solutions for nonlinear evolutionary systems of mixed type ⋮
On the problem of two linearized wells ⋮
Analysis of the Minimal Traveling Wave Speed via the Methods of Young Measures ⋮
Direct approach to the problem of strong local minima in calculus of variations ⋮
Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture ⋮
\({\mathcal {A}}\)-free rigidity and applications to the compressible Euler system ⋮
Weak convergence theory for strong materials with \(p(x)\)-growth ⋮
Integral functionals with \(p(x)\)- and \(p(x,u)\)-growth ⋮
Lower semicontinuity via \(W^{1,q}\)-quasiconvexity ⋮
Incompatible sets of gradients and metastability ⋮
A note on measure-valued solutions to the full Euler system. ⋮
Existence of entropy measure-valued solutions for forward-backward \(p\)-parabolic equations ⋮
Weak Lower Semicontinuity of Integral Functionals and Applications ⋮
Singular perturbations of forward-backward \(p\)-parabolic equations ⋮
On lower semicontinuity in \(BH^p\) and 2-quasiconvexification ⋮
Generalized $W^{1,1}$-Young Measures and Relaxation of Problems with Linear Growth ⋮
Analysis of microstructures and phase transition phenomena in one-dimensional, non-linear elasticity by convex optimization ⋮
Relaxation of optimal control problems in Lp-SPACES ⋮
Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys ⋮
Necessary and sufficient conditions for the strong local minimality of C1 extremals on a class of non-smooth domains ⋮
Closed 𝓐-pQuasiconvexity and Variational Problems with Extended Real-Valued Integrands ⋮
Sequential weak continuity of null Lagrangians at the boundary ⋮
A new approach to Young measure theory, relaxation and convergence in energy ⋮
On rank-one convex and polyconvex conformal energy functions with slow growth ⋮
Conditions on integral functional implying validity of the theory of weak convergence ⋮
Limits of inner superposition operators and Young measures ⋮
Young Measures as Measurable Functions and Their Applications to Variational Problems ⋮
A note on locking materials and gradient polyconvexity ⋮
Lower semicontinuity and relaxation for integral functionals with \(p(x)\)- and \(p(x, u)\)-growth ⋮
Hashin–Shtrikman bounds and their attainability for multi-phase composites ⋮
Young measure solutions for a class of forward-backward convection-diffusion equations ⋮
An evolutionary double-well problem ⋮
Oscillations and concentrations generated by ${\mathcal A}$-free mappings and weak lower semicontinuity of integral functionals ⋮
Nonlocal variational principles ⋮
Orlicz equi-integrability for scaled gradients ⋮
On convergence of gradient-dependent integrands. ⋮
Unnamed Item ⋮
Characterization of generalized Young measures generated by symmetric gradients ⋮
Mathematics Behind Microstructures: A Lead to Generalizations of Convexity ⋮
Young measures supported on invertible matrices ⋮
Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy ⋮
Linear approximation for equations of motion of vibrating membrane with one parameter ⋮
Characterization of two-scale gradient Young measures and application to homogenization ⋮
Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms ⋮
Multi-materials with strong interface: Young measures formulation ⋮
Linear-programming approach to nonconvex variational problems ⋮
Coarse-Convex-Compactification Approach to Numerical Solution of Nonconvex Variational Problems ⋮
Local minimizers and quasiconvexity -- the impact of topology ⋮
Young measure solutions of some nonlinear mixed-type equations ⋮
A refinement on existence results in nonconvex optimal control ⋮
Young-measure quasi-static damage evolution ⋮
Equi-integrability results for 3D-2D dimension reduction problems ⋮
Mesoscopic model of microstructure evolution in shape memory alloys, its numerical analysis and computer implementation ⋮
Characterization of generalized gradient Young measures generated by sequences in \(W^{1,1}\) and BV ⋮
Oscillations and concentrations in sequences of gradients ⋮
Atomistic to Continuum limits for computational materials science ⋮
Characterization of gradient young measures generated by homeomorphisms in the plane ⋮
PROJECTIONS ONTO THE CONE OF OPTIMAL TRANSPORT MAPS AND COMPRESSIBLE FLUID FLOWS ⋮
A local proof for the characterization of Young measures generated by sequences in BV ⋮
Vector variational problems and applications to optimal design ⋮
Existence of solutions to the \(A\)-Laplace system via Young measures ⋮
Effective energy integral functionalsfor thin films on curl-free vector fields in the Orlicz–Sobolev space setting ⋮
Γ-convergence and absolute minimizers for supremal functionals ⋮
Characterization of generalized Young measures generated by \({\mathcal{A}} \)-free measures ⋮
Quasiconvexity in the fractional calculus of variations: characterization of lower semicontinuity and relaxation ⋮
Numerical approaches to rate-independent processes and applications in inelasticity ⋮
Young measure approach to characterization of behaviour of integral functionals on weakly convergent sequences by means of their integrands ⋮
Null Lagrangian measures in subspaces, compensated compactness and conservation laws ⋮
Homogenization of periodic nonconvex integral functionals in terms of Young measures ⋮
Sets of lower semicontinuity and stability of integral functionals ⋮
Deriving new evolution equations for microstructures via relaxation of variational incremental problems ⋮
Quasi-linear parabolic systems in divergence form with weak monotonicity ⋮
Existence of minimisers of variational problems posed in spaces of mixed smoothness ⋮
Modelling of Thin Martensitic Films with Nonpolynomial Stored Energies ⋮
Differential Inclusions and Young Measures Involving Prescribed Jacobians ⋮
Quasilinear degenerated elliptic system in divergence form with mild monotonicity in weighted Sobolev spaces ⋮
Sharp stability results for almost conformal maps in even dimensions ⋮
Relaxation for optimal design problems with non-standard growth ⋮
Higher integrability of minimizing Young measures ⋮
Optimization, relaxation and Young measures ⋮
A necessary and sufficient condition for lower semicontinuity ⋮
Oscillation and concentration in sequences of PDE constrained measures ⋮
Numerical approximation of young-measure solutions to parabolic systems of forward-backward type ⋮
Gradient Young measures generated by sequences in Sobolev spaces ⋮
A sharp interface evolutionary model for shape memory alloys ⋮
Which measure-valued solutions of the monoatomic gas equations are generated by weak solutions? ⋮
Measure-Valued Low Mach Number Limits of Ideal Fluids ⋮
Dissipative Measure-Valued Solutions to the Euler–Poisson Equation ⋮
Probabilistic descriptions of fluid flow: a survey ⋮
Young measures generated by sequences in Morrey spaces ⋮
Quasiconvexity at the boundary and the nucleation of austenite
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