Stochastic PDEs via convex minimization

Abstract

We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle [50] to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a parameter-dependent convex functional on entire trajectories. Its unique minimizers correspond to elliptic-in-time regularizations of the stochastic differential problem. As the regularization parameter tends to zero, solutions of the limiting problem are recovered. This in particular provides a direct approch via convex optimization to the approximation of nonlinear stochastic partial differential equations.

Locations

• Communications in Partial Differential Equations - View - PDF
• arXiv (Cornell University) - View - PDF
• Virtual Community of Pathological Anatomy (University of Castilla La Mancha) - View - PDF
• DataCite API - View