Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution
Analysis of PDEs
2017-12-25 v1 Probability
Abstract
A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line with the standard parabolic theory.
Keywords
Cite
@article{arxiv.1712.08196,
title = {Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution},
author = {H. -J. Kim and S. V. Lototsky},
journal= {arXiv preprint arXiv:1712.08196},
year = {2017}
}