Graph properties for nonlocal minimal surfaces
By Serena Dipierro, Ovidiu Savin, Enrico Valdinoci. 2015
48 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/adc2f33fc8a4b7cf9ec7105ad30a1edc185a912c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Nicola Abatangelo
- Enrico Valdinoci
- Xavier Ros-Oton
- Giovanni Molica Bisci
- Gerd Grubb
- Serena Dipierro
- Binlin Zhang
- Raffaella Servadei
In Computational Theory and Mathematics
- Nicola Abatangelo
- Enrico Valdinoci
- Xavier Ros-Oton
- Gerd Grubb
- Giovanni Molica Bisci
- Raffaella Servadei
- Binlin Zhang
- A. Fiscella
Citations in the corpus
- Getting Acquainted with the Fractional Laplacian (2017, background): “Other important differences between the classical and fractional cases arise in the study of nonlocal minimal surfaces and in related fields: just to list a few features, differently than in the classical case, nonlocal minimal surfaces typically “stick” at the boundary, see [38,40], nonlocal cateno”