On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder
Analysis of PDEs
2011-07-01 v1
Abstract
We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero cylinder condition. We prove a regularity result after finding suitable spaces for the solution and the pre-assigned datum in the problem. The tools from potential theory, harmonic analysis and probability are used. Some Lemmas are as important as the main Theorem.
Keywords
Cite
@article{arxiv.1106.6125,
title = {On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder},
author = {Tongkeun Chang and Kijung Lee and Minsuk Yang},
journal= {arXiv preprint arXiv:1106.6125},
year = {2011}
}