Analysis Seminar

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Dimensional bounds and rectifiability for measure solutions to PDEs

Speaker: Filip Rindler, Warwick

Location: Warren Weaver Hall 1314

Date: Thursday, September 5, 2019, 9:45 a.m.

Synopsis:

Under-determined PDEs of the form A\mu = \sigma, where A is a linear constant-coefficient PDE operator, appear in many different problems of geometric measure theory and the calculus of variations, e.g. in the structure theory of normal currents (A=div), varifolds, BV maps (A=curl) and BD maps (A=curlcurl). In this talk I will show some recent results combining harmonic analysis and geometric measure theory methods, that give general (and optimal) dimensional bounds and rectifiability results for such PDE-constrained measures.