Second-order elliptic equations with variably partially VMO coefficients

By Nicolai V. Krylov. 2008

73 citations recorded by the source corpus.

Abstract The solvability in W p 2 ( R 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4df2faa30717ca1b5c4f0f0b41e56c838b88918a

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Elliptic and parabolic equations for measures (2009, background): “It is worth noting that some of the conditions on A employed above can be relaxed by using the results in [107], [108], [109].”
Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains (2011, methodology): “6 below is from [29] and can be considered as a generalized version of the Fefferman-Stein Theorem.”
Elliptic equations with measurable coefficients in Reifenberg domains (2010, result): “In what concerns divergence and non-divergence form elliptic and parabolic operators whose coefficients are measurable in one variable and VMO with respect to the others, we would like to mention a series of recent works [11,12,17–19] where D.”
Elliptic Equations in Divergence Form with Partially BMO Coefficients (2008, methodology): “Very recently, their result was generalized by Krylov [19], where the leading coefficients are assumed to be measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball.”
Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficients (2011, background): “The theory of elliptic and parabolic equations with partially VMO coefficients was originated in Kim and Krylov [13].”