Perron's method for pathwise viscosity solutions
Analysis of PDEs
2018-06-19 v5
Abstract
We use Perron's method to construct viscosity solutions of fully nonlinear degenerate parabolic pathwise (rough) partial differential equations. This provides an intrinsic method for proving the existence of solutions that relies only on a comparison principle, rather than considering equations driven by smooth approximating paths. The result covers the case of multidimensional geometric rough path noise, where the noise coefficients depend nontrivially on space and on the gradient of the solution. Also included in this note is a discussion of the comparison principle and a summary of the pathwise equations for which one has been proved.
Keywords
Cite
@article{arxiv.1605.01108,
title = {Perron's method for pathwise viscosity solutions},
author = {Benjamin Seeger},
journal= {arXiv preprint arXiv:1605.01108},
year = {2018}
}
Comments
Minor edits. To appear in CPDE