Symmetrization of exterior parabolic problems and probabilistic interpretation
Analysis of PDEs
2016-10-20 v1
Abstract
We prove a comparison theorem for the averages of the solutions of two exterior parabolic problems, the second being the "symmetrization" of the first one, by using approximation of the Schwarz symmetrization by polarizations, as it was introduced in [4]. This comparison provides an alternative proof, based on PDEs, of the isoperimetric inequality for the Wiener sausage, which was proved in [14].
Keywords
Cite
@article{arxiv.1604.01747,
title = {Symmetrization of exterior parabolic problems and probabilistic interpretation},
author = {Konstantinos Dareiotis},
journal= {arXiv preprint arXiv:1604.01747},
year = {2016}
}
Comments
13 pages