Parabolic regularity and Dirichlet boundary value problems

DOI10.1016/j.na.2019.03.014zbMath1416.35058arXiv1707.01001OpenAlexW2964133791MaRDI QIDQ2312568

Martin Dindoš, Luke Dyer

Publication date: 17 July 2019

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01001

zbMATH Keywords

time-varying cylinders

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20)

Cites Work

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• A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations
• Some properties of nonnegative solutions of parabolic differential operators
• Estimates of harmonic measure
• The \(L^p\) regularity problem for the heat equation in non-cylindrical domains
• The Neumann problem for elliptic equations with non-smooth coefficients
• Behavior near the boundary of positive solutions of second order parabolic equations
• The Dirichlet boundary problem for second order parabolic operators satisfying a Carleson condition
• BMO solvability and the \(A_\infty\) condition for second order parabolic operators
• Boundary value problems and duality between \(L^p\) Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains
• \(L^ 2\) solvability and representation by caloric layer potentials in time-varying domains
• The Dirichlet problem for parabolic operators with singular drift terms
• THE INITIAL DIRICHLET BOUNDARY VALUE PROBLEM FOR GENERAL SECOND ORDER PARABOLIC SYSTEMS IN NONSMOOTH MANIFOLDS
• The Initial-Neumann Problem for the Heat Equation in Lipschitz Cylinders
• The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders
• Weakly Differentiable Functions
• Generalized Parabolic Functions using the Perron-Wiener-Brelot Method
• The Dirichlet problem for second order parabolic operators
• 𝐿²-solvability of the Dirichlet, Neumann and regularity problems for parabolic equations with time-independent Hölder-continuous coefficients
• The method of layer potentials for the heat equation in time-varying domains
• Perturbation and Solvability of Initial L^p Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains
• Singular integrals with mixed homogeneity
• 𝐿^{𝑝} boundary value problems for parabolic equations