The <inline-formula><tex-math id="M1"> C^1,α </tex-math></inline-formula> boundary Harnack principle in a slit domain and its application to the Signorini problem

2023/07/24 by Chilin Zhang, Zhang, Chilin
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.3934/cpaa.2026063

Abstract

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

Citations

• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

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