Minimization of a fractional perimeter-Dirichlet integral functional
Caffarelli, Luis ; Savin, Ovidiu ; Valdinoci, Enrico
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015), p. 901-924 / Harvested from Numdam
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We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely ∫ Ω|∇u(x)| 2 dx+ Per σ ({u>0},Ω), with σ∈(0,1). We obtain regularity results for the minimizers and for their free boundaries ∂{u>0} using blow-up analysis. We will also give related results about density estimates, monotonicity formulas, Euler–Lagrange equations and extension problems.

@article{AIHPC_2015__32_4_901_0,
     author = {Caffarelli, Luis and Savin, Ovidiu and Valdinoci, Enrico},
     title = {Minimization of a fractional perimeter-Dirichlet integral functional},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {32},
     year = {2015},
     pages = {901-924},
     doi = {10.1016/j.anihpc.2014.04.004},
     mrnumber = {3390089},
     zbl = {1323.35216},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2015__32_4_901_0}
}

Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico. Minimization of a fractional perimeter-Dirichlet integral functional. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) pp. 901-924. doi : 10.1016/j.anihpc.2014.04.004. http://gdmltest.u-ga.fr/item/AIHPC_2015__32_4_901_0/

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