Regularity for weak solutions to nondiagonal quasilinear degenerate elliptic systems

2014/04/25 by Yan Dong, Dong, Yan, Pengcheng Niu +1
Mathematics · #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1404.6425

arxiv created 2014/04/25 · arxiv updated 2014/04/28

Abstract

The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to Hörmander's vector fields, where the coefficients are bounded with vanishing mean oscillation. We first prove L^p(p ≥ 2) estimates for gradients of weak solutions by using a priori estimates and a known reverse Hölder inequality, and consider regularity to the corresponding nondiagonal homogeneous degenerate elliptic systems. Then we get higher Morrey and Campanato estimates for gradients of weak solutions to original systems and Hölder estimates for weak solutions.

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