The Dirichlet boundary problem for second order parabolic operators satisfying Carleson condition

Abstract

We establish $L^p$, $2\le p\le \infty$ solvability of the Dirichlet boundary value problem for a parabolic equation $u_t-\mbox{div}(A\nabla u)=0$ on time-varying domains with coefficient matrix $A=(a_{ij})$ that satisfy a small Carleson condition. The result is motivated by similar results for the elliptic equation $\mbox{div}(A\nabla u)=0$ that were established previously.

References in corpus (3)

• Initial-Boundary Value Problems for Parabolic Equations
• BMO solvability and the $A_{\infty }$ condition for second order parabolic operators
• Square Functions and the $A_{\infty }$ Property of Elliptic Measures

Cited by in corpus (3)

• Partial regularity and smooth topology-preserving approximations of rough domains
• BMO solvability and the $A_{\infty }$ condition for second order parabolic operators
• Regularity theory for solutions to second order elliptic operators with complex coefficients and the $L^p$ Dirichlet problem