Convex integration for diffusion equations and Lipschitz solutions of polyconvex gradient flows
From MaRDI portal
Publication:786067
DOI10.1007/s00526-020-01785-7zbMath1445.35223OpenAlexW3041441629MaRDI QIDQ786067
Publication date: 12 August 2020
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-020-01785-7
Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convex integration for the Monge-Ampère equation in two dimensions
- Lack of uniqueness for weak solutions of the incompressible porous media equation
- The Euler equations as a differential inclusion
- Quasiconvexity and partial regularity in the calculus of variations
- Convexity conditions and existence theorems in nonlinear elasticity
- Implicit partial differential equations
- General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases
- On \(W^{1,p}\)-solvability for special vectorial Hamilton--Jacobi systems.
- Convex integration for Lipschitz mappings and counterexamples to regularity
- A proof of Onsager's conjecture
- On Lipschitz solutions for some forward-backward parabolic equations
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Two-phase solutions for one-dimensional non-convex elastodynamics
- The regularity of critical points of polyconvex functionals
- Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics
- On Lipschitz solutions for some forward-backward parabolic equations. II: The case against Fourier
- Parabolic systems with nowhere smooth solutions
- Existence of infinitely many solutions for the one-dimensional Perona-Malik model
- On existence of weak solutions for one-dimensional forward-backward diffusion equations
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Convex integration for a class of active scalar equations
- Partial Differential Relations
- Strict convexity, strong ellipticity, and regularity in the calculus of variations
- Weak Convergence of Integrands and the Young Measure Representation
- Studying Nonlinear pde by Geometry in Matrix Space
- Young Measure Solutions for a Nonlinear Parabolic Equation of Forward-Backward Type
- The regularity of general parabolic systems with degenerate diffusion
- Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions
- Diffeomorphisms and Nonlinear Heat Flows
- Semicontinuity problems in the calculus of variations
- Direct methods in the calculus of variations
- Optimal existence theorems for nonhomogeneous differential inclusions
- A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy
This page was built for publication: Convex integration for diffusion equations and Lipschitz solutions of polyconvex gradient flows
