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arXiv · 2212.01339

H\"{o}lder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network

Xiangsheng Xu
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Abstract

In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The system is singular and involves cubic nonlinearity. Our investigation reveals that weak solutions are H\"{o}lder continuous when the space dimension $N$ is $2$. This is achieved via an inequality associated with the Stummel-Kato class of functions and refinement of a lemma originally due to S. Campanato and C. B. Morrey (\cite{G}, p. 86).

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Xiangsheng Xu. 2022-12-02. H\"{o}lder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network. https://arxiv.org/abs/2212.01339

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