Second-order elliptic equations with variably partially VMO coefficients
Copyright policy )Second-order elliptic equations with variably partially VMO coefficients
The solvability in $W^{2}_{p}(\bR^{d})$ 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.
17 pages. Auxiliary results slightly reorganized. Few misprints corrected
- University of Minnesota United States
- University of Minnesota Morris United States
- University of Minnesota System United States
- University of Minesota United States
- University of Minnesota United States
Partially VMO coefficients, Vanishing mean oscillation, Existence of generalized solutions of PDE, partially VMO coefficients, Second-order elliptic equations, Mathematics - Analysis of PDEs, Sobolev spaces, 35J15, vanishing mean oscillation, FOS: Mathematics, second-order elliptic equations, Analysis, Analysis of PDEs (math.AP)
Partially VMO coefficients, Vanishing mean oscillation, Existence of generalized solutions of PDE, partially VMO coefficients, Second-order elliptic equations, Mathematics - Analysis of PDEs, Sobolev spaces, 35J15, vanishing mean oscillation, FOS: Mathematics, second-order elliptic equations, Analysis, Analysis of PDEs (math.AP)
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