Lecture Notes
Inserted: 18 nov 2024
Last Updated: 19 jan 2025
Journal: to appear
Year: 2025
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.
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