Analysis Seminar

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Direct epiperimetric inequalities for the classical and thin obstacle problem

Speaker: Maria Colombo, IAS

Location: Warren Weaver Hall 1314

Date: Thursday, November 14, 2019, 9:45 a.m.

Synopsis:

We study the regularity of the regular and of the singular set of some
free boundary problems in any dimension. To this end we introduce a new
tool, which we call _logarithmic epiperimetric inequality_, which works
also at singular points. It allows to study the regularity of the
singular set and yields an explicit logarithmic modulus of continuity on
the $C^{^1}$ regularity (which is optimal in general), thus improving the
known regularity and providing a fully alternative method.
In turn, the logarithmic epiperimetric inequality follows from a
suitable Lojasiewicz inequality for a (non-analytic) constrained
functional associated to the obstacle problem.