A gradient estimate for nonlocal minimal graphs

DOI10.1215/00127094-2018-0052zbMath1421.53011arXiv1711.08232OpenAlexW3100395783WikidataQ128265828 ScholiaQ128265828MaRDI QIDQ2631560

Matteo Cozzi, Xavier Cabré

Publication date: 15 May 2019

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08232

zbMATH Keywords

gradient estimatesrigidity theoremsregularity resultsnonlocal minimal surfacesfractional Sobolev inequalitiesnonlocal minimal graphsweak Harnack inequalities

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Length, area, volume, other geometric measure theory (28A75) Integro-differential operators (47G20)

Related Items (16)

Boundary properties of fractional objects: flexibility of linear equations and rigidity of minimal graphs ⋮ Finite element algorithms for nonlocal minimal graphs ⋮ On the growth of nonlocal catenoids ⋮ Some perspectives on (non)local phase transitions and minimal surfaces ⋮ Nonlocal minimal graphs in the plane are generically sticky ⋮ Boundary continuity of nonlocal minimal surfaces in domains with singularities and a problem posed by Borthagaray, Li, and Nochetto ⋮ The stickiness property for antisymmetric nonlocal minimal graphs ⋮ Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory ⋮ Fractional elliptic problems on Lipschitz domains: regularity and approximation ⋮ Regularity results for nonlocal minimal surfaces ⋮ A fractional Michael-Simon Sobolev inequality on convex hypersurfaces ⋮ Regularity results for nonlocal equations and applications ⋮ The stickiness phenomena of nonlocal minimal surfaces: new results and a comparison with the classical case ⋮ Finite element discretizations of nonlocal minimal graphs: Convergence ⋮ On nonlocal minimal graphs ⋮ Linear and nonlinear fractional elliptic problems

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