Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem ☆

Abstract

In this paper, we study solutions u of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder Q+1 subset of Rn+1, where the coefficients are weighted by x alpha n, alpha is an element of (-infinity, 1). We establish higher-order boundary Schauder type estimates of x alpha nu under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with H & ouml;lder continuous coefficients. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.