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arXiv · 2004.00337

Stochastic PDEs via convex minimization

Luca Scarpa·Ulisse Stefanelli
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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.

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Luca Scarpa, Ulisse Stefanelli. 2020-04-01. Stochastic PDEs via convex minimization. https://doi.org/10.1080/03605302.2020.1831017

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