Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization

DOI10.1007/BF03377405zbMath1386.35174arXiv1611.04321OpenAlexW2951343937MaRDI QIDQ1691847

Michael Loss, Jean Dolbeault, Maria J. Esteban

Publication date: 25 January 2018

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04321

zbMATH Keywords

symmetryweightsinstabilityrate of convergencefast diffusion equationasymptotic behaviorself-similar solutionslinearizationbifurcationspectral gapsymmetry breakingentropy methodsoptimal constantsself-similar variablesrigidity resultsCaffarelli-Kohn-Nirenberg inequalitiesspectral estimatesGagliardo-Nirenberg inequalitiesHardy-Poincaré inequalitycarré du champparabolic flowsintermediate asymptoticsoptimal functionsentropy -- entropy production inequalityimproved inequalitiesRényi entropy powers

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items

Improved interpolation inequalities and stability, Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations, Parabolic methods for ultraspherical interpolation inequalities, Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case, Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results

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