Global regularity in Orlicz-Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients
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We show continuity in generalized Orlicz-Morrey spaces MΦ,φ(ℝn) of sublinear integral operators generated by Calderón-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 L = ∑ni,j=1 aij(x)Dij with discontinuous coefficients. We show that Lu ∈ MΦ,φ implies the second-order derivatives belong to MΦ,φ.
CitationGuliyev, V. S., Ahmadli, A. A., Omarova, M. N., & Softova, L. (2018). Global regularity in Orlicz-Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients. Electronic Journal of Differential Equations, 2018(110), pp. 1-24.
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