Can one prove uniqueness for boundary value problems of PDEs that do not have regular solutions?

Abstract: In this talk, I want to explain the yes answer to the title by looking at a class of elliptic linear problems of Dirichlet type. The strategy is one one could take using Green’s kernels or fundamental solutions and we show that it can still be used at an operator level and uniqueness depends on having enough solutions of a dual problem. This talk is based on joint works with Moritz Egert.

Bio: A professor at Paris-Sud University since 2002, Pascal Auscher is specialized in harmonic analysis and contributed both to the wavelet theory and partial differential equations. He was involved in proving the Kato conjecture. Along with his research, he headed the Laboratoire amiénois de mathématique fondamentale et appliquée (LAMFA) between 2000 and 2002. From 2006, he was in charge of assessing laboratories and training programs in his discipline on behalf of the French Ministry of Research before becoming (from 2007 to 2009) a scientific representative at the former AERES (agency for the evaluation of research and higher education. A member of the scientific board of the INSMI between 2010 and 2014, Pascal Auscher also coordinated an International Associated Laboratory with Australia, prior to becoming Director of the Institute in August 2017.


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