Parabolic equations with measurable coefficients

Abstract

We investigate the unique solvability of second order parabolic equations in non-divergence form in $W_p^{1,2}((0,T) \times \bR^d)$, $p\ge 2$. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.

19 pages

References in corpus (3)

• A'priori estimates and precise regularity for parabolic systems with discontinuous data
• W^{2,1}_p Solvability for Parabolic Poincare Problem
• Parabolic equations with measurable coefficients in $L_p$-spaces with mixed norms

Cited by in corpus (7)

• Elliptic equations in divergence form with partially BMO coefficients
• Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains
• Optimal Control of Conditional Value-at-Risk in Continuous Time
• Solvability of second-order equations with hierarchically partially BMO coefficients
• Parabolic equations with measurable coefficients in $L_p$-spaces with mixed norms
• Parabolic equations with partially VMO coefficients and boundary value problems in Sobolev spaces with mixed norms
• Recent progress in the $L_p$ theory for elliptic and parabolic equations with discontinuous coefficients