We are interested in proving the regularity of solutions to some systems of reaction--diffusion equations, which is actually a consequence of global boundedness.
Our approach is inspired by De Giorgi's method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere adaptation of scalar techniques; in particular the entropy dissipation of the system plays a crucial role in the analysis.
Copyright. All Rights Reserved.