H\"{o}lder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network
Analysis of PDEs
2022-12-05 v1
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 is . 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).
Keywords
Cite
@article{arxiv.2212.01339,
title = {H\"{o}lder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network},
author = {Xiangsheng Xu},
journal= {arXiv preprint arXiv:2212.01339},
year = {2022}
}