Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs
Analysis of PDEs
2024-06-06 v1
Abstract
This article investigates the exceptional set of the boundary for the following problem: \begin{equation*} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{\lambda,\Lambda}^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \rm{in} ~ \Omega_{T}, \end{aligned} \end{equation*} We provide a sufficient condition on the exceptional set in terms of the bound of the Hausdorff measure of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.
Keywords
Cite
@article{arxiv.2406.03481,
title = {Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs},
author = {Ram Baran Verma and Mohan Mallick},
journal= {arXiv preprint arXiv:2406.03481},
year = {2024}
}