Lower estimates of \(L^{\infty}\)-norm of gradients for Cauchy problems

DOI10.1016/J.JMAA.2017.08.045zbMath1457.35013OpenAlexW2759483887MaRDI QIDQ1682085

Yasuhiro Fujita

Publication date: 28 November 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.08.045

zbMATH Keywords

optimalitylogarithmic Sobolev inequalityHamilton-Jacobi equationslower estimatesparabolic equationsLipschitz constants

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) Initial value problems for second-order parabolic equations (35K15) Initial value problems for nonlinear first-order PDEs (35F25) Hamilton-Jacobi equations (35F21)

Related Items (3)

A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality ⋮ A Dynamical Approach to Lower Gradient Estimates for Viscosity Solutions of Hamilton–Jacobi Equations ⋮ An improvement of level set equations via approximation of a distance function

Cites Work

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• An optimal logarithmic Sobolev inequality with Lipschitz constants
• Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift
• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• Global Lipschitz regularizing effects for linear and nonlinear parabolic equations
• Asymptotic Solutions of Hamilton–Jacobi Equations with Semi-Periodic Hamiltonians
• Bounds for the fundamental solution of a parabolic equation

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