Given a connected bounded open Lipschitz set Ω⊂R2, we show that the relaxed Cartesian area functional A(u,Ω) of a map u∈W1,1(Ω;S1) is finite, and we provide a useful upper bound for its value. Using this estimate, we prove a modified version of a De Giorgi conjecture adapted to W1,1(Ω;S1), on the largest countably subadditive set function A(u,⋅) smaller than or equal to A(u,⋅).
Bellettini, G., Scala, R., Scianna, G. (2024). Upper bounds for the relaxed area of S1-valued Sobolev maps and its countably subadditive interior envelope. REVISTA MATEMATICA IBEROAMERICANA, 40(6), 2135-2178 [10.4171/RMI/1475].
Upper bounds for the relaxed area of S1-valued Sobolev maps and its countably subadditive interior envelope
Giovanni Bellettini;Riccardo Scala;Giuseppe Scianna
2024-01-01
Abstract
Given a connected bounded open Lipschitz set Ω⊂R2, we show that the relaxed Cartesian area functional A(u,Ω) of a map u∈W1,1(Ω;S1) is finite, and we provide a useful upper bound for its value. Using this estimate, we prove a modified version of a De Giorgi conjecture adapted to W1,1(Ω;S1), on the largest countably subadditive set function A(u,⋅) smaller than or equal to A(u,⋅).
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11365/1276839