Gross's Logarithmic Sobolev Inequality: A Simple Proof

DOI10.2307/2374139zbMath0421.46029OpenAlexW2331977974MaRDI QIDQ3854172

Frank H. Clarke, Robert A. Adams

Publication date: 1979

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374139

zbMATH Keywords

quantum field theoryGaussian measurehypercontractive inequalityGross's logarithmic Sobolev inequalityroyal road of Caratheodory

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Constructive quantum field theory (81T08) Hamilton-Jacobi theories (49L99) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (12)

On grand and small Lebesgue and Sobolev spaces and some applications to PDE's ⋮ General logarithmic Sobolev inequalities and Orlicz imbeddings ⋮ A note on the proof by adams and clarke of gross's logarithmic sobolev inequality ⋮ Bobkov’s Inequality via Optimal Control Theory ⋮ Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators ⋮ Logarithmic Sobolev inequality revisited ⋮ Convergence from power-law to logarithm-law in nonlinear scalar field equations ⋮ Optimal Gaussian Sobolev embeddings ⋮ Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere ⋮ Orbital stability of standing waves for some nonlinear Schrödinger equations ⋮ On hypercontractivity for multipliers on orthogonal polynomials ⋮ A proof of a logarithmic Sobolev inequality

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