Higher order parabolic systems with piecewise DMO and Hölder continuous coefficients

2024/07/25 by Dong, Hongjie, Li, Haigang, Xu, Longjuan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.17733

Abstract

In this paper, we are concerned with divergence form, higher-order parabolic systems in a cylindrical domain with a finite number of subdomains. We establish L_∞ and Schauder estimates of solutions when the leading coefficients and the non-homogeneous term exhibit piecewise Dini mean oscillation and piecewise Hölder continuity, respectively. To the best of our knowledge, our results are new for higher-order elliptic and parabolic systems.

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