Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets

2024/05/12 by Yuanyuan Lian, Lian, Yuanyuan · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2405.07214

openalex publication_date 2024/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain the interior pointwise C^k,α (k≥ 0, 0<α<1) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness method and perturbation technique are employed. The pointwise regularity is proved in a very simple way and the results are optimal. In addition, these pointwise regularity can be used to characterize the structure of the nodal sets of solutions.

Cited by

• A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
• Boundary Regularity for Fully Nonlinear Parabolic equations on C^1,Dini Domains

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