Calculus of Variations and Geometric Measure Theory

A. Figalli - A. Guerra - S. Kim - H. Shahgholian

Constraint Maps and Free Boundaries

created by figalli on 18 Nov 2024

[BibTeX]

Lecture Notes

Inserted: 18 nov 2024
Last Updated: 18 nov 2024

Journal: Preprint
Year: 2024

Abstract:

Free boundary problems emerge in various fields of partial differential equations. These problems occur when the behavior of variables changes abruptly at certain values. Numerous examples abound, such as the solid-liquid interface during material solidification, the boundary between exercise and continuation regions of a financial instrument (like an American option), and the transition from elastic to plastic behavior when stress surpasses a critical threshold. These applications often lead to free boundary problems being referred to as phase transition problems.


Download: