Edgard A. Pimentel, José Miguel Urbano
Published 2020-07-16Version 1
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 $\mathcal{C}^{1,\text{log-Lip}}$-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.
Comments: Manuscript accepted for publication in Ann. Sc. Norm. Super. Pisa Cl. Sci
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