University of Birmingham > Talks@bham > Analysis Seminar > Higher regularity for the thin obstacle problem

Higher regularity for the thin obstacle problem

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Thin obstacle problems arise in the modelling of many chemical, physical and financial problems. In this talk I will present a new, robust strategy of proving optimal regularity for low regularity coefficients. Here the central new tool is a Carleman inequality which replaces an Almgren type monotonicity formula. With the optimal regularity at hand, I will discuss quantitative higher regularity results for the thin obstacle problem in the presence of Hölder coefficients. Crucial ingredients in this context are a Hodograph-Legendre transform, the analysis of a fully nonlinear degenerate elliptic equation and the introduction of suitable function spaces. This is joint work with H. Koch and W. Shi.

This talk is part of the Analysis Seminar series.

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