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2022 The Thin Obstacle Problem: A Survey
Xavier Fernández-Real
Publ. Mat. 66(1): 3-55 (2022). DOI: 10.5565/PUBLMAT6612201

Abstract

In this work we present a general introduction to the Signorini problem (or thin obstacle problem). It is a self-contained survey that aims to cover the main currently known results regarding the thin obstacle problem. We present the theory with some proofs, from the optimal regularity of solutions and classification of free boundary points to more recent results on the non-regular part of the free boundary and generic regularity.

Funding Statement

This work has received funding from the European Research Council (ERC) under Grant Agreement No 721675, and from the Swiss National Science Foundation under SNF Grant 200021_182565

Funding Statement

This work has received funding from the European Research Council (ERC) under Grant Agreement No 721675, and from the Swiss National Science Foundation under SNF Grant 200021_182565

Funding Statement

This work has received funding from the European Research Council (ERC) under Grant Agreement No 721675, and from the Swiss National Science Foundation under SNF Grant 200021_182565

Citation

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Xavier Fernández-Real. "The Thin Obstacle Problem: A Survey." Publ. Mat. 66 (1) 3 - 55, 2022. https://doi.org/10.5565/PUBLMAT6612201

Information

Received: 18 June 2020; Accepted: 6 November 2020; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612201

Subjects:
Primary: 347G20 , 35R35

Keywords: fractional obstacle problem , free boundary , Signorini problem , survey , thin obstacle problem

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.66 • No. 1 • 2022
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