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Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. (English) Zbl 0917.35017

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.

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.)
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