Existence and improved regularity for a nonlinear system with collapsing ellipticity

2020/07/16 by Edgard A. Pimentel, Pimentel, Edgard A., José Miguel Urbano +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2007.08462

Manuscript accepted for publication in Ann. Sc. Norm. Super. Pisa Cl. Sci

arxiv created 2020/07/16 · arxiv updated 2020/07/17

Abstract

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 C^1,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.

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