Irregularity and non-uniqueness: a differential inclusions approach

speaker: László Székelyhidi (Universität Bonn)

abstract: In this minicourse we present a general approach in the framework of compensated compactness to extract information on oscillatory behaviour of solutions to certain nonlinear systems of PDEs. We show how to use this information in connection with convex integration to construct regularity and uniqueness counterexamples in some rather surprising contexts. These range from the Nash-Kuiper theory of isometric embeddings and the existence of smooth elliptic systems with nowhere C1 solutions, to the non-uniqueness of dissipative weak solutions of the Euler equations and sharpness examples for the Lp norm of singular integrals.

timetable:
Mon 7 Sep, 9:30 - 10:30, Aula Dini
Mon 7 Sep, 11:00 - 12:00, Aula Dini
Tue 8 Sep, 9:30 - 10:30, Aula Dini
Tue 8 Sep, 11:00 - 12:00, Aula Dini
Wed 9 Sep, 9:30 - 10:30, Aula Dini
Wed 9 Sep, 11:00 - 12:00, Aula Dini
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