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