We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an improved C1,Log-Lip regularity estimate using tangential analysis methods. The system illustrates a sophisticated version of the proverbial thermistor problem and our results are new even in simpler modelling scenarios.
|Number of pages
|Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
|Published - Jan 1 2021