Urbana Campus Research Calendar (OVCRI)

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Harmonic Analysis and Differential Equations Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Altgeld Hall 143
Date
Apr 30, 2024   1:00 pm  
Speaker
Cristian Enache (American University of Sharjah)
Contact
Carrie Clark
E-Mail
carriec2@illinois.edu
Views
74
Originating Calendar
Harmonic Analysis and Differential Equations Seminar (HADES)

Speaker: Cristian Enache (American University of Sharjah) https://www.aus.edu/faculty/cristian-enache

Title: A survey on the maximum principle and its applications

Abstract:

In this talk we will survey some old and new results on the maximum principles (especially for for P-functions) and their applications to the study of partial differential equations. More precisely, we will show how one can employ the maximum principle in problems of physical or geometrical interest, in order to get the shape of some free boundaries, isoperimetric inequalities, symmetry results, convexity results and Liouville type results. In the first part of the talk  we'll be mainly focused on some overdetermined problems, while in the second part of the talk we'll present some of our contributions to some Monge-Ampere type problems. Finally, we will discuss some open problems where the use of the maximum principle might be useful.

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