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, cilt.43, sa.4, ss.14-31, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 4
  • Basım Tarihi: 2023
  • Dergi Adı: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.14-31
  • Anahtar Kelimeler: fractional maximal operator, generalized Morrey spaces, small BMO, Nonlinear elliptic equations, Reifenberg flat domain
  • Ankara Üniversitesi Adresli: Evet

Özet

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.