Parabolic equations in simple convex polytopes with time irregular coefficients

Abstract

We prove the $W_p^{1,2}$-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when $p\in (1,2]$. We also consider the corresponding Neumann problem in a half space when $p\in [2,\infty )$. Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions.

31 pages, submitted

References in corpus (3)

• Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains
• Solvability of second-order equations with hierarchically partially BMO coefficients
• On elliptic equations in a half space or in convex wedges with irregular coefficients