Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 43, Issue 6, Pages 998-1018Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2018.1488262
Keywords
stochastic partial differential equations; viscosity solutions; non-linear parabolic equations; existence problems; comparison principle
Categories
Funding
- National Science Foundation (NSF) Research Training Group (RTG) [DMS1246999]
- NSF [DMS-1266383, DMS-1600129]
- Office of Naval Research (ONR) [N000141712095]
Ask authors/readers for more resources
We use Perron's method to construct viscosity solutions of fully non-linear 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 non-trivially 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available