73 citations · 125 across the 11 of their papers we have counts for
15 papers
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…
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…
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…
Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations
Farhan Abedin, Russell W. Schwab
We establish that the regularity theory for translation invariant fractional order parabolic integro-differential equations (via Krylov-Safonov estimates) gives an improv…
Min-max formulas for nonlocal elliptic operators on Euclidean space
Nestor Guillen, Russell Schwab
An operator satisfies the Global Comparison Property if anytime a function touches another from above at some point, then the operator preserves the ordering at the point of contac…
Some free boundary problems recast as nonlocal parabolic equations
Hector A. Chang-Lara, Nestor Guillen, Russell W. Schwab
In this work we demonstrate that a class of some one and two phase free boundary problems can be recast as nonlocal parabolic equations on a submanifold. The canonical examples wou…
Estimates for Dirichlet-to-Neumann maps as integro-differential operators
Nestor Guillen, Jun Kitagawa, Russell W. Schwab
Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or…
Min-max formulas for nonlocal elliptic operators
Nestor Guillen, Russell W. Schwab
In this work, we give a characterization of Lipschitz operators on spaces of functions (also , , , ) that obey the global comparison property--…
Neumann Homogenization via Integro-Differential Operators, Part 2: singular gradient dependence
Nestor Guillen, Russell W. Schwab
We continue the program initiated in a previous work, of applying integro-differential methods to Neumann Homogenization problems. We target the case of linear periodic equations w…
Regularity for parabolic integro-differential equations with very irregular kernels
Russell W. Schwab, Luis Silvestre
We prove Hölder regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof which avoids the use…
Neumann Homogenization via Integro-Differential Operators
Nestor Guillen, Russell W. Schwab
In this note we describe how the Neumann homogenization of fully nonlinear elliptic equations can be recast as the study of nonlocal (integro-differential) equations involving elli…
Hölder Regularity For Integro-Differential Equations With Nonlinear Directional Dependence
Marcus Rang, Moritz Kassmann, Russell W. Schwab
We prove Hölder regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dep…
Regularity results for nonlocal parabolic equations
Moritz Kassmann, Russell W. Schwab
We survey recent regularity results for parabolic equations involving nonlocal operators like the fractional Laplacian. We extend the results of Felsinger-Kassmann (2013) and obtai…
Stochastic Homogenization for Some Nonlinear Integro-Differential Equations
Russell W. Schwab
In this note we extend to the random, stationary ergodic setting previous results of periodic homogenization for a particular family of nonlinear nonlocal "elliptic" equations with…
Aleksandrov-Bakelman-Pucci Type Estimates For Integro-Differential Equations
Nestor Guillen, Russell Schwab
In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations, the proof of which relies on an…