Variational Problems with Long-Range Interaction - Archive ouverte HAL Access content directly
Journal Articles Archive for Rational Mechanics and Analysis Year : 2017

Variational Problems with Long-Range Interaction

(1) , (2) , (3) , (4)
1
2
3
4

Abstract

We consider a class of variational problems for densities that repel each other at distance. Typical examples are given by the Dirichlet functional and the Rayleigh functional D(u) = k i=1 ˆΩ |∇u i | 2 or R(u) = k i=1 ´Ω |∇u i | 2 ´Ω u 2 i minimized in the class of H 1 (Ω, R k) functions attaining some boundary conditions on ∂Ω, and subjected to the constraint dist({u i > 0}, {u j > 0}) 1 ∀i = j. For these problems, we investigate the optimal regularity of the solutions, prove a free-boundary condition, and derive some preliminary results characterizing the free boundary ∂{ k i=1 u i > 0}.
Fichier principal
Vignette du fichier
1701.05005.pdf (581.02 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03884821 , version 1 (05-12-2022)

Identifiers

Cite

Nicola Soave, Hugo Tavares, Susanna Terracini, Alessandro Zilio. Variational Problems with Long-Range Interaction. Archive for Rational Mechanics and Analysis, 2017, 228 (3), pp.743-772. ⟨10.1007/s00205-017-1204-2⟩. ⟨hal-03884821⟩
0 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More