The general optimal \(L^{p}\)-Euclidean logarithmic Sobolev inequality by Hamilton–Jacobi equations. (English) Zbl 1173.35424
The author presents a general optimal \(L^p\)-Euclidean logarithmic Sobolev inequality by using the Prẹkopa-Leinder inequality and a special Hamilton-Jacobi equation.
Reviewer: Messoud A. Efendiev (Berlin)
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
Logarithmic Sobolev inequality; Prékopa–Leindler inequality; Hamilton–Jacobi equations; Optimal constantsReferences:
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