Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term

Michael Salins; Samy Tindel

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arXiv · 2302.10678

Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term

Michael Salins·Samy Tindel

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Abstract

We prove the existence of density for the solution to the multiplicative semilinear stochastic heat equation on an unbounded spatial domain, with drift term satisfying a half-Lipschitz type condition. The methodology is based on a careful analysis of differentiability for a map defined on weighted functional spaces.

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Michael Salins, Samy Tindel. 2023-02-21. Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term. https://arxiv.org/abs/2302.10678

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