Free Boundary Problems
Obstacle problems, Stefan problems, and regularity of free boundaries.
Free Boundary Problems. Obstacle problems, Stefan problems, and regularity of free boundaries.
Foundations and canonical references
The standard treatments of free boundary problems approach the subject from complementary angles. Caffarelli, A Geometric Approach to Free Boundary Problems (2005) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for free boundary problems include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2005A Geometric Approach to Free Boundary Problemscaffarelli-2005, salsa-2005
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