Parabolic equations with measurable coefficients in $L_p$-spaces with mixed norms

Abstract

The unique solvability of parabolic equations in Sobolev spaces with mixed norms is presented. The second order coefficients (except $a^{11}$) are assumed to be only measurable in time and one spatial variable, and VMO in the other spatial variables. The coefficient $a^{11}$ is measurable in one spatial variable and VMO in the other variables.

Cited by in corpus (2)

• Second-order elliptic equations with variably partially VMO coefficients
• Parabolic equations with partially VMO coefficients and boundary value problems in Sobolev spaces with mixed norms