A comparison principle for a class of doubly nonlinear parabolic fractional partial differential equations

Michael Strunk

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arXiv · 2606.31618

A comparison principle for a class of doubly nonlinear parabolic fractional partial differential equations

Michael Strunk

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Abstract

In this paper, we establish a comparison principle for non-negative weak solutions to a class of doubly nonlinear parabolic fractional partial differential equations within a space-time cylinder $\Omega_T=\Omega\times(0,T)\subset\mathbb{R}^{n+1}$. For the two solutions considered, we assume that at least one of them is time-independent outside the spatial domain, i.e. in $\Omega^{c}=\mathbb{R}^n\setminus\Omega$. As an application of this result, we readily infer the uniqueness of a non-negative weak solution to the corresponding Cauchy-Dirichlet problem.

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Michael Strunk. 2026-06-30. A comparison principle for a class of doubly nonlinear parabolic fractional partial differential equations. https://arxiv.org/abs/2606.31618

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