Nonlinear elliptic equations with integro-differential divergence form operators and measure data under sign condition on the nonlinearity

2021/11/08 by Klimsiak, Tomasz
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.04393

Abstract

We study existence problem for semilinear equations with Borel measure data and operator generated by a symmetric Markov semigroup. We assume merely that the nonlinear part satisfies the so-called sign condition. Using the method of sub and supersolutions we show the existence of maximal measure for which there exists a solution to the problem (the so-called reduced measure introduced by H. Brezis, M. Marcus and A.C. Ponce).

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• Generalized solutions to semilinear elliptic equations with measure data
• Measure Differential Equation with a Nonlinear Growth/Decay Term
• Selected problems on elliptic equations involving measures
• Minkowski problem arising from sub-linear elliptic equations
• Existence and stability of solutions of general semilinear elliptic equations with measure data