Hölder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network

2022/12/02 by Xiangsheng Xu, Xu, Xiangsheng
Engineering · Environmental Science · Mathematics · #Analysis of PDEs (math.AP) #Ecosystem dynamics and resilience #FOS: Mathematics #Mathematical Biology Tumor Growth #Slime Mold and Myxomycetes Research

paper · pdf · doi:10.48550/arxiv.2212.01339

openalex publication_date 2022/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hölder 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 (\citeG, p. 86).

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