Publications

Stochastic PDEs via convex minimization

Author(s)
Luca Scarpa, Ulisse Stefanelli
Abstract

We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle 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 approach via convex optimization to the approximation of nonlinear stochastic partial differential equations.

Organisation(s)
Department of Mathematics, Research Platform Accelerating Photoreaction Discovery
External organisation(s)
Institute of Genetics and Biophysics "Adriano Buzzati-Traverso", CNR
Journal
Communications in Partial Differential Equations
Volume
46
Pages
66-97
No. of pages
32
ISSN
0360-5302
DOI
https://doi.org/10.1080/03605302.2020.1831017
Publication date
2021
Peer reviewed
Yes
Austrian Fields of Science 2012
101002 Analysis
Keywords
ASJC Scopus subject areas
Analysis, Applied Mathematics
Portal url
https://ucrisportal.univie.ac.at/en/publications/6ec43a9b-66db-4855-a39f-ac4b656a77c8