Fan, Dashan; Lu, Shanzhen; Yang, Dachun Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. (English) Zbl 0917.35017 Georgian Math. J. 5, No. 5, 425-440 (1998). The aim of the paper is to provide a global \(L^{p,\lambda}\) theory for the Dirichlet problem for the elliptic equation \(a_{ij}(x) u_{x_ix_j} = f\), assuming \(a_{ij} \in L^\infty \cap VMO\) in a bounded domain with mild boundary. Although the authors use techniques already introduced in previous papers (see the references therein), Theorem 2.1 is interesting from a functional-theoretical point of view. The paper, in general, is correct but the crucial point which makes the difference with the interior regularity case – namely estimate 3.5 – is stated but not proved. Reviewer: G.Di Fazio (Catania) Cited in 1 ReviewCited in 51 Documents MSC: 35B65 Smoothness and regularity of solutions to PDEs 35J25 Boundary value problems for second-order elliptic equations 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) Keywords:singular integrals; commutator PDFBibTeX XMLCite \textit{D. Fan} et al., Georgian Math. J. 5, No. 5, 425--440 (1998; Zbl 0917.35017) Full Text: EuDML EMIS