Sharp estimates for the gradient of solutions to the heat equation

DOI10.1090/SPMJ/1610zbMath1446.35047arXiv1808.03101OpenAlexW3023676074MaRDI QIDQ5108694

Gershon I. Kresin, Vladimir Gilelevich Maz'ya

Publication date: 6 May 2020

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03101

zbMATH Keywords

heat equationfirst and second boundary value problemssharp pointwise estimates for gradient

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20) A priori estimates in context of PDEs (35B45) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (2)

Sharp pointwise estimates for the gradients of solutions to linear parabolic second order equation in the layer ⋮ Sharp pointwise estimates for solutions of weakly coupled second-order parabolic system in a layer

Cites Work

• Optimal pointwise stimates for derivatives of solutions to Laplace, Lamé, and Stokes equations
• Sharp real-part theorems. A unified approach. Translated from Russian and edited by T. Shaposhnikova
• Invariant convex bodies for strongly elliptic systems
• An extremal problem for integrals on a measure space with abstract parameters
• Sharp real-part theorems in the upper halfplane and similar estimates for harmonic functions
• Generalized Poisson integral and sharp estimates for harmonic and biharmonic functions in the half-space

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