We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the assumption of convexity. On the other hand, in the nonlocal framework, stickiness is “generic”. We provide various examples from the literature, and focus on the case of complete stickiness in highly nonlocal regimes.
The stickiness phenomena of nonlocal minimal surfaces: New results and a comparison with the classical case / C. Bucur. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - 10:1(2019 Dec 31), pp. 42-82. [10.6092/ISSN.2240-2829/10362]
The stickiness phenomena of nonlocal minimal surfaces: New results and a comparison with the classical case
C. Bucur
2019
Abstract
We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the assumption of convexity. On the other hand, in the nonlocal framework, stickiness is “generic”. We provide various examples from the literature, and focus on the case of complete stickiness in highly nonlocal regimes.
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