Mathematics > Analysis of PDEs
[Submitted on 2 Dec 2022
]
Title: Hölder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network
Title: 弱解在模拟生物运输网络的椭圆-抛物线系统中的Hölder连续性
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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