Regularity of solutions to nonlinear thin and boundary obstacle problems

2021/05/03 by Luca Di Fazio, Emanuele Spadaro, Di Fazio, Luca +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.01005

openalex publication_date 2021/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Variational inequalities with thin obstacles and Signorini-type boundary conditions are classical problems in the calculus of variations, arising in numerous applications. In the linear case many refined results are known, while in the nonlinear setting our understanding is still at a preliminary stage. In this paper we prove C¹ regularity for the solutions to a general class of quasi-linear variational inequalities with thin obstacles and C^{1, α} regularity for variational inequalities under Signorini-type conditions on the boundary of a domain.

Related

• On the nonlinear thin obstacle problem
• C^1,α estimates for the fully nonlinear Signorini problem
• The Thin Obstacle Problem: A Survey
• Optimal regularity for the Signorini problem
• Almost minimizers for the thin obstacle problem