Some notes on functions of least Ws,1-fractional seminorm

Autor: Claudia Bucur

Publikováno v: Bruno Pini Mathematical Analysis Seminar, Vol 14, Iss 1, Pp 38-57 (2023)

In this survey we discuss some existence and asymptotic results, originally obtained in [4,3], for functions of least Ws,1-fractional seminorm. We present the connection between these functions and nonlocal minimal surfaces, leveraging this relation

Externí odkaz: https://doaj.org/article/d8e20ff4fb9243e886ad946a19532160

Enhanced boundary regularity of planar nonlocal minimal graphs and a butterfly effect

Autor: Serena Dipierro, Aleksandr Dzhugan, Nicolò Forcillo, Enrico Valdinoci

Publikováno v: Bruno Pini Mathematical Analysis Seminar, Vol 11, Iss 1, Pp 44-67 (2020)

In this note, we showcase some recent results obtained in [DSV19] concerning the stickiness properties of nonlocal minimal graphs in the plane. To start with, the nonlocal minimal graphs in the planeenjoy an enhanced boundary regularity, since bounda

Externí odkaz: https://doaj.org/article/858b86ac1cbd4d7f88b5a96cbcb373ce

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Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory

Autor: Xavier Cabré

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

For nonnegative even kernels $K$, we consider the $K$-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated $K$-nonlocal mean curvature equation in an open set $\Omega\subset\

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e5bd6329d0958b624a1425d1cd79965
https://doi.org/10.1007/s10231-020-00952-z

Stable s-minimal cones in ℝ3 are flat for s ~ 1

Autor: Joaquim Serra, Eleonora Cinti, Xavier Cabré

Publikováno v: Journal für die reine und angewandte Mathematik, 764 (2020)
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

We prove that half spaces are the only stable nonlocal s-minimal cones in ℝ3, for s∈(0,1) sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof cannot rely on a compactn

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c4cd94770837d11dbe66507515943e8
https://hdl.handle.net/20.500.11850/426602