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arXiv · 2407.17733

Higher order parabolic systems with piecewise DMO and H\"{o}lder continuous coefficients

Hongjie Dong·Haigang Li·Longjuan Xu
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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 $L_\infty$ and Schauder estimates of solutions when the leading coefficients and the non-homogeneous term exhibit piecewise Dini mean oscillation and piecewise H\"{o}lder continuity, respectively. To the best of our knowledge, our results are new for higher-order elliptic and parabolic systems.

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Hongjie Dong, Haigang Li, Longjuan Xu. 2024-07-25. Higher order parabolic systems with piecewise DMO and H\"{o}lder continuous coefficients. https://arxiv.org/abs/2407.17733

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