Graph Properties for Nonlocal Minimal Surfaces
نویسندگان
چکیده
In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension 3, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler-Lagrange equation related to the nonlocal mean curvature.
منابع مشابه
Boundary Behavior of Nonlocal Minimal Surfaces
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and convex. This is a purely nonlocal phenomenon, and it is in sharp contrast with the boundary properties of the classical minimal surfaces. In particular, we s...
متن کاملDigital cohomology groups of certain minimal surfaces
In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...
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 کاملNONLOCAL 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 کامل