3 papers
math.AP2026
Partial Hölder regularity for fully nonlinear nonlocal parabolic equations with integrable kernels
Minhyun Kim, Luke Schleef, Russell W. Schwab
In this work, we consider solutions to (fully nonlinear) parabolic integro-differential equations with integrable interaction kernels. A typical equation would be that obtained by…
math.AP2025
Hamilton-Jacobi-Bellman equations on graphs
Nicolò Forcillo, Jun Kitagawa, Russell W. Schwab
Here, we study Hamilton-Jacobi-Bellman equations on graphs. These are meant to be the analog of any of the following types of equations in the continuum setting of partial differen…
math.AP2025
Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions
Russell Schwab, Son Tu, Olga Turanova
In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravit…