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

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 ([5] , p. 86). [ABSTRACT FROM AUTHOR]