W^{2,1}_p Solvability for Parabolic Poincare Problem

Abstract

We study Poincaré problem for a linear uniformly parabolic operator $\P$ in a cylinder $Q=\Omega \times (0,T).$ The boundary operator $\B$ is defined by an oblique derivative with respect to a tangential vector field $ł$ defined on the lateral boundary $S.$ The coefficients of $\P$ are supposed to be $VMO$ away from the set of tangency $E$ and to possess higher regularity in $x$ near to $E.$ A unique strong solvability result is obtained in $W_p^{2,1}(Q)$ for all $p\in (1,\infty ).$

13 pages

Cited by in corpus (2)

• Parabolic equations with measurable coefficients
• Parabolic equations with partially VMO coefficients and boundary value problems in Sobolev spaces with mixed norms