Second-order elliptic equations with variably partially VMO coefficients

作者：Krylov N V^*

来源：Journal of Functional Analysis, 2009, 257(6): 1695-1712.

DOI：10.1016/j.jfa.2009.06.014

• Second-order elliptic equations
• Vanishing mean oscillation
• Partially VMO coefficients
• Sobolev spaces

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.

• 出版日期2009-9-15