Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces

Abstract In this paper we study elliptic and parabolic boundary value problems with inhomogeneous conditions in weighted function spaces of Sobolev, Bessel potential, Besov Triebel-Lizorkin type. As one the main results, solve problem L q -maximal regularity for case, where spatial weight is a power Muckenhoupt $A_{\infty }$ A ∞ -class. space case have restriction that microscopic parameter equals to . Going beyond A p -range, integrability or under consideration, yields extra flexibility sharp inhomogeneities. This allows us treat rougher data provides quantitative smoothing effect on interior domain. The ingredient an analysis anisotropic Poisson operators.