Joint BCAM-UPV/EHU Analysis and PDE seminar: On global solutions of the obstacle problem and the behaviour of the regular part of the free boundary close to singularities

LOCATION: BCAM Seminar room and Online

Abstract
In this talk we investigate global solutions of the classical obstacle problem. I give a partial result (under some dimension bound) towards a conjecture by H. Shahgholian ('92) saying that the coincidence sets of global solutions of the obstacle problem are in the closure of ellipsoids, i.e. ellipsoids, paraboloids, cylinders with one of the two as basis, or half-spaces. I will briefly sketch the proof and then present - as a corollary - a new characterization of the behaviour of the regular part of the free boundary in the obstacle problem close to singularities of certain types.


Link to the session: 
https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09

More info at https://sites.google.com/view/apdebilbao/home