Global regularity in Orlicz-Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients

We show continuity in generalized Orlicz-Morrey spaces MΦ,ϕ(ℝn) of sublinear integral operators generated by Calder´on-Zygmund operator and their commutators with BMO functions. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operator (Formula presented.) with discontinuous coefficients. We show that Lu ∈ MΦ, φ implies the second-order derivatives belong to MΦ,φ. © 2018 Texas State University

Authors
Guliyev V.S. 1, 2, 3 , Ahmadli A.A.4 , Omarova M.N.5 , Softova L.6
Journal
Electronic Journal of Differential Equations
Language
English
Pages
1-24
Status
Published
Link
External link
Volume
2018
Year
2018
Organizations
  • 1 Ahi Evran University, Department of Mathematics, Kirsehir, 40100, Turkey
  • 2 S.M. Nikol’skii Institute of Mathematics at RUDN University, Moscow, 117198, Russian Federation
  • 3 Institute of Mathematics and Mechanics, Baku, Az 1141, Azerbaijan
  • 4 Dumlupinar University, Department of Mathematics, Kytahya, 40100, Turkey
  • 5 Baku State University, Baku, AZ1141, Azerbaijan
  • 6 Department of Civil Engineering, Second University of Naples, Italy
Keywords
Calder´on-Zygmund integrals; Commutators; Dirichlet problem; Elliptic equations; Generalized Orlicz-Morrey spaces; VMO
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