Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains

2019/07/25 by Jinping Zhuge, Zhuge, Jinping
Computer Science · Mathematics · #35B50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1907.10857

openalex publication_date 2019/07/25 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

In dimension two or three, the weak maximum principal for biharmonic equation is valid in any bounded Lipschitz domains. In higher dimensions (greater than three), it was only known that the weak maximum principle holds in convex domains or C¹ domains, and may fail in general Lipschitz domains. In this paper, we prove the weak maximum principle in higher dimensions in quasiconvex Lipschitz domains, which is a sharp condition in some sense and recovers both convex and C¹ domains.

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