russell schwab's index page
research interests:
Analysis of nonlinear PDE and Probability Theory and their relationships to understanding multiscale systems. This includes nonlinear elliptic, parabolic, Hamilton-Jacobi, and elliptic integro-differential equations and their corresponding associated stochastic processes. Also of interest are nonlinear stochastic PDEs, in the class of parabolic and Hamilton-Jacobi equations. In general I am interested in new analysis and applications of PDEs.
preprints and publications:
(1) Stochastic Homogenization of Hamilton-Jacobi Equations in Stationary Ergodic Spatio-Temporal Media -- Indiana University Mathematics Journal
(2) Periodic Homogenization For Nonlinear Integro-Differential Equations, -- SIAM Journal of Mathematical Analysis
(3) Aleksandrov-Bakelman-Pucci Type Estimates For Integro-Differential Equations, (Joint with Nestor Guillen) -- arXiv:1101.0279v2 [math.AP]
(4) Stochastic Homogenization for Some Nonlinear Integro-Differential Equations, -- arXiv:1101.6052v1 [math.AP]
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