Second-order elliptic equations with variably partially VMO coefficients

2008/07/06 by Н. В. Крылов, Krylov, N. V. · 2 citations
Mathematics · Computer Science · #Advanced Mathematical Physics Problems #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0807.0926

Abstract

The solvability in W²_p(\bR^d) spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients.

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• On some divergence-form singular elliptic equations with codimension-two boundary: L^p-estimates
• Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space

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