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arXiv · 2504.01794

On the regularity of entropy solutions to stochastic degenerate parabolic equations

Marko Erceg·Kenneth H. Karlsen·Darko Mitrović
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Abstract

We study the regularity of entropy solutions for quasilinear parabolic equations with anisotropic degeneracy and stochastic forcing. Building on previous works, we establish space-time regularity under a non-degeneracy condition that does not require an assumption on the derivative of the symbol of the corresponding kinetic equation, a restriction imposed in earlier studies. This allows us to obtain regularity results for certain equations not accounted for by prior theory, albeit with reduced regularity exponents. Our approach uses a kinetic formulation with two transport equations, one of second order and one of first order, leveraging a form of "parabolic regularity" inherent in these equations that was not utilized in previous studies.

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Marko Erceg, Kenneth H. Karlsen, Darko Mitrović. 2025-04-02. On the regularity of entropy solutions to stochastic degenerate parabolic equations. https://arxiv.org/abs/2504.01794

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