Logarithmic Sobolev Trace Inequalities
F. Feo, M.R. Posteraro

TL;DR
This paper establishes a new logarithmic Sobolev trace inequality in Gaussian spaces, analyzes the trace operator in weighted Sobolev spaces, and explores applications to partial differential equations, demonstrating the sharpness of the results.
Contribution
It introduces a novel logarithmic Sobolev trace inequality in Gaussian spaces and examines the trace operator in weighted Sobolev spaces with applications to PDEs.
Findings
Proved a sharp logarithmic Sobolev trace inequality in Gaussian space.
Analyzed the trace operator in weighted Sobolev spaces.
Applied results to partial differential equations.
Abstract
We prove a logarithmic Sobolev trace inequality in a gaussian space and we study the trace operator in the weighted Sobolev space W^{1,p}(\Omega,\gamma) for sufficiently regular domain. We exhibit examples to show the sharpness of the results. Applications to PDE are also considered.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems
