On the nonlinear thin obstacle problem

2024/03/28 by Anna Abbatiello, Abbatiello, Anna, Giovanna Andreucci +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2403.19487

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The thin obstacle problem or n-dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly quadratic energies, whereas only partial results have been proved in the nonlinear case. In this paper we consider the thin boundary obstacle problem for a general class of nonlineraities and we prove the optimal C^{1, (1)/(2)}-regularity of the solutions in any space dimension.

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