Upper bounds for the relaxed area of S¹ -valued Sobolev maps and its countably subadditive interior envelope.

Autor:	Bellettini, Giovanni, Scala, Riccardo, Scianna, Giuseppe
Předmět:	MINIMAL surfaces SET functions LOGICAL prediction
Zdroj:	Revista Mathematica Iberoamericana; 2024, Vol. 40 Issue 6, p2135-2178, 44p
Abstrakt:	Given a connected bounded open Lipschitz set Ω ⊂ R², we show that the relaxed Cartesian area functional A̅ (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 ... (u,⋅) smaller than or equal to A̅ (u,⋅). [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
Externí odkaz:	Zobrazit plný text záznamu