English

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

Analysis of PDEs 2021-11-09 v1

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).

Keywords

Cite

@article{arxiv.2111.04393,
  title  = {Nonlinear elliptic equations with integro-differential divergence form operators and measure data under sign condition on the nonlinearity},
  author = {Tomasz Klimsiak},
  journal= {arXiv preprint arXiv:2111.04393},
  year   = {2021}
}