Injections de Sobolev probabilistes et applications

2011/11/30 by Burq, Nicolas, Lebeau, Gilles · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.7310

Abstract

In this article, we give probabilistic versions of Sobolev embeddings on any Riemannian manifold (M,g). More precisely, we prove that for natural probability measures on L²(M), almost every function belong to all spaces L^p(M), p

Cited by

• Universal Cancellations in Uniform Random Waves
• On the supremum of random cusp forms
• Almost Sure Uniform Convergence Of Random Hermite Series

Related

• Geometrical properties of the space P_f(X) of probability measures
• Monotone invariants and embeddings of statistical manifolds
• Sobolev embedding for M^1,p spaces is equivalent to a lower bound of the measure
• Compactness of higher-order Sobolev embeddings
• Sobolev embedding implies regularity of measure in metric measure spaces