The $ C^{1,\alpha} $ boundary Harnack principle in a slit domain and its application to the Signorini problem

Communications on Pure &amp Applied Analysis 2026 Open access

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Authors: Chilin Zhang
DOI: 10.3934/cpaa.2026063
Cited by: 0
References: 18

Abstract

We prove the $ C^{2, \alpha} $ regularity of the free boundary in the Signorini problem with variable coefficients. We use a $ C^{1, \alpha} $ boundary Harnack inequality in slit domains. The key method is to study a non-standard degenerate elliptic equation and obtain a $ C^{1, \alpha} $ Schauder estimate.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Advanced Harmonic Analysis Research Advanced Mathematical Modeling in Engineering

Publication details

Journal / source
Communications on Pure &amp Applied Analysis
Volume
35
Issue
0
Pages
23–47
Publication date
1 January 2026
Language
EN