On the variation of the fractional mean curvature under the effect of \(C^{1, \alpha}\) perturbations

DOI10.3934/dcds.2015.35.5769zbMath1335.35274OpenAlexW2524246500MaRDI QIDQ255563

Matteo Cozzi

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.5769

zbMATH Keywords

fractional Laplacian\(C^{1,\alpha}\)-diffeomorphism\(s\)-perimeterfractional mean curvaturenon-local equationsquantitative implicit function theorem

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75) Implicit function theorems, Jacobians, transformations with several variables (26B10) Fractional partial differential equations (35R11)

Related Items (10)

\(K\)-mean convex and \(K\)-outward minimizing sets ⋮ Regularity and Bernstein-type results for nonlocal minimal surfaces ⋮ Convex sets evolving by volume-preserving fractional mean curvature flows ⋮ Local Hölder regularity of minimizers for nonlocal variational problems ⋮ Nonlocal capillarity for anisotropic kernels ⋮ The divergence theorem and nonlocal counterparts ⋮ Neckpinch singularities in fractional mean curvature flows ⋮ Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter ⋮ Boundary behavior of nonlocal minimal surfaces ⋮ (Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property

Cites Work

• Unnamed Item
• Unnamed Item
• Local and global minimizers for a variational energy involving a fractional norm
• Regularity of nonlocal minimal cones in dimension 2
• Asymptotics of the \(s\)-perimeter as \(s \searrow 0\)
• Hitchhiker's guide to the fractional Sobolev spaces
• \(\Gamma \)-convergence for nonlocal phase transitions
• Uniform estimates and limiting arguments for nonlocal minimal surfaces
• Gamma-convergence of nonlocal perimeter functionals
• Regularity results for nonlocal equations by approximation
• A nonlocal anisotropic model for phase transitions
• The gradient theory of phase transitions and the minimal interface criterion
• A fractional framework for perimeters and phase transitions
• Gevrey regularity for integro-differential operators
• Regularity and Bernstein-type results for nonlocal minimal surfaces
• Regularity properties of nonlocal minimal surfaces via limiting arguments
• Anisotropic fractional perimeters
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• A Notion of Nonlocal Curvature
• Nonlocal minimal surfaces
• Regularity theory for fully nonlinear integro-differential equations
• A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies
• Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
• An Extension Problem Related to the Fractional Laplacian
• Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions

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