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.
Originalsprache | Englisch |
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Seiten (von - bis) | 66-97 |
Seitenumfang | 32 |
Fachzeitschrift | Communications in Partial Differential Equations |
Jahrgang | 46 |
Ausgabenummer | 1 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2021 |
ÖFOS 2012
- 101002 Analysis