2 May, Thursday
John McSorley
Finding unitype graphs amongst uncyclic graphs
Monday, April 29, 2024
Wednesday, April 10, 2024
Spring 2024
11 Apr 2024
18 Apr 2024
25 Apr 2024
Mathew Gluck
The role of compactness in partial differential equations having variational structure
Abstract: A partial differential operator is said to be variational if it can be realized as the differential of some scalar-valued functional. For partial differential equations involving variational operators, exhibiting the existence of solutions is equivalent to exhibiting the existence of critical points of the associated functional. A key tool in exhibiting the existence of critical points is compactness. In short, compactness allows one to pass from a sequence of approximate critical points to a genuine critical point. I will illustrate this concept in multiple settings, starting with an undergraduate-level problem and ending with a variational partial differential equation that one might see in a graduate-level course. Finally, I will discuss a variational problem where there is no apriori compactness. For this problem, I will emphasize how the failure of compactness can be overcome.
Thursday, April 4, 2024
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