Well-posedness and regularity of stochastic heat equations on moving domains

Chongyang Ren; Tusheng Zhang

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arXiv · 2608.27166

Well-posedness and regularity of stochastic heat equations on moving domains

Chongyang Ren·Tusheng Zhang

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Abstract

In this paper we investigate stochastic heat equations driven by multiplicative noise on moving domains. We establish the well-posedness within a nonhomogeneous variational framework. Furthermore, by combining stochastic De Giorgi iteration with Dirichlet parabolic estimates, we obtain the H\"older regularity of the solutions.

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Chongyang Ren, Tusheng Zhang. 2026-08-27. Well-posedness and regularity of stochastic heat equations on moving domains. https://arxiv.org/abs/2608.27166

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