Obstacle type problems for minimal surfaces
L. Caffarelli, D. De Silva, O. Savin
TL;DR
This paper investigates obstacle problems related to minimal surfaces, both standard and nonlocal, establishing optimal regularity of solutions and characterizing the free boundary to advance understanding of these geometric variational problems.
Contribution
It provides new regularity results and free boundary characterizations for obstacle problems involving minimal surfaces, including nonlocal variants.
Findings
Optimal regularity of solutions established
Characterization of the free boundary achieved
Applicable to both standard and nonlocal minimal surfaces
Abstract
We study certain obstacle type problems involving standard and nonlocal minimal surfaces. We obtain optimal regularity of the solution and a characterization of the free boundary.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Differential Equations and Boundary Problems