Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions

DOI10.1137/15M1012220zbMath1320.35243arXiv1503.00772WikidataQ59163419 ScholiaQ59163419MaRDI QIDQ5264066

Baisheng Yan, Seonghak Kim

Publication date: 20 July 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.00772

zbMATH Keywords

differential inclusionconvex integrationBaire's category methodinitial-Neumann boundary value problem

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Computing methodologies for image processing (68U10) Initial-boundary value problems for second-order parabolic equations (35K20) Weak solutions to PDEs (35D30) Initial-boundary value problems for PDEs of mixed type (35M13) Boundary value problems for systems of nonlinear first-order PDEs (35F60)

Related Items (18)

Interfacial phenomena of the forward backward convection-diffusion equations ⋮ On one-dimensional forward-backward diffusion equations with linear convection and reaction ⋮ On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems ⋮ On Lipschitz solutions for some forward-backward parabolic equations. II: The case against Fourier ⋮ On a gradient maximum principle for some quasilinear parabolic equations on convex domains ⋮ On Lipschitz solutions for some forward-backward parabolic equations ⋮ Very weak solutions of the Dirichlet problem for the two dimensional Monge-Ampère equation ⋮ On nonuniqueness and nonregularity for gradient flows of polyconvex functionals ⋮ Three examples of residual pathologies ⋮ Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations ⋮ Bounded solutions of ideal MHD with compact support in space-time ⋮ Two-phase solutions for one-dimensional non-convex elastodynamics ⋮ Mixing solutions for the Muskat problem ⋮ Convex integration for the Monge-Ampère equation in two dimensions ⋮ A gradient maximum principle of solutions for a quasilinear parabolic equation ⋮ On weak closure of some diffusion equations ⋮ Convex integration for diffusion equations and Lipschitz solutions of polyconvex gradient flows ⋮ Numerical approximation of young-measure solutions to parabolic systems of forward-backward type

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