Regularity of nonlocal minimal cones in dimension 2
نویسندگان
چکیده
منابع مشابه
NONLOCAL s-MINIMAL SURFACES AND LAWSON CONES
Here 0 < s < 1, χ designates characteristic function, and the integral is understood in the principal value sense. The classical notion of minimal surface is recovered by letting s → 1. In this paper we exhibit the first concrete examples (beyond the plane) of nonlocal s−minimal surfaces. When s is close to 1, we first construct a connected embedded s-minimal surface of revolution in R, the non...
متن کاملRegularity and Bernstein-type results for nonlocal minimal surfaces
We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi [5] stating that the validity of Bernstein’s theorem in dimension n + 1 is a consequence of the nonexistence of n-dimensional singular minimal cones in IR.
متن کاملNonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness
We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior regularity and rigidity properties, in a quantitative and qualitative way, and their (perhaps rather surprising) boundary behavior. We present at least a sketch of the proofs of these results, in a way that aims to be as elementary and self contained as possible, referring to the papers [CRS10, SV1...
متن کاملRegularity of minimizers for three elliptic problems: minimal cones, harmonic maps, and semilinear equations
We discuss regularity issues for minimizers of three nonlinear elliptic problems. They concern minimal cones, minimizing harmonic maps into a hemisphere, and radial local minimizers of semilinear elliptic equations. We describe the strong analogies among the three regularity theories. They all use a method originated in a paper of J. Simons on the area minimizing properties of cones.
متن کاملStable Solutions of the Allen-cahn Equation in Dimension 8 and Minimal Cones
For all n ≥ 1, we are interested in bounded solutions of the AllenCahn equation ∆u + u − u3 = 0 which are defined in all Rn+1 and whose zero set is asymptotic to a given minimal cone. In particular, in dimension n+1 ≥ 8, we prove the existence of stable solutions of the Allen-Cahn equation whose zero sets are not hyperplanes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2012
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-012-0539-7