H\"older estimates of weak solutions to degenerate chemotaxis systems with a source term

TL;DR

This paper establishes H"older continuity for bounded solutions of degenerate chemotaxis systems with porous media diffusion and source terms, covering both parabolic-parabolic and elliptic-parabolic cases.

Contribution

It provides the first regularity results for solutions to chemotaxis systems with porous media type diffusion and Hadamard growth source terms.

Findings

Proves H"older regularity for bounded solutions.

Applies to both parabolic-parabolic and elliptic-parabolic systems.

Extends regularity theory to systems with degenerate diffusion and growth conditions.

Abstract

In this note we consider degenerate chemotaxis systems with porous media type diffusion and a source term satisfying the Hadamard growth condition. We prove the H\"older regularity for bounded solutions to parabolic-parabolic as well as for elliptic-parabolic chemotaxis systems.