Regularity of solutions to nonlinear elliptic equations in generalized Morrey spaces

Akbulut A., Gadjiev T. S., ŞERBETÇİ A., Rustamov Y. I.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.43, no.4, pp.14-31, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 4
  • Publication Date: 2023
  • Journal Name: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.14-31
  • Keywords: fractional maximal operator, generalized Morrey spaces, small BMO, Nonlinear elliptic equations, Reifenberg flat domain
  • Ankara University Affiliated: Yes

Abstract

In this paper, we prove the generalized Morrey estimates for the gradient of weak solutions to a class of nonlinear elliptic equations in a very general irregular domain. The nonlinearity a(x, ξ) is assumed to be measurable in x for almost every ξ and belongs to the small BMO class.