2D Thin obstacle problem with data at infinity

2022/01/05 by Runcao Lyu, Zikai Ye, Lyu, Runcao +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2201.01465

openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the thin obstacle problem in ℝ² with data at infinity. We first prove the existence and uniqueness of it. Then we show that its symmetric solutions are actually half-space solutions. Our results are needed when classifying the half-space (2k-(1)/(2))-homogeneous solutions to the thin obstacle problems in ℝ³. It is a generalization of one part of Savin-Yu's work \citesavin2021halfspace on classifying the half-space (7)/(2)-homogeneous solutions.

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