Minimization of a fractional perimeter-Dirichlet integral functional
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 4, p. 901-924
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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.

DOI : https://doi.org/10.1016/j.anihpc.2014.04.004
Keywords: Free boundary problems, Fractional minimal surfaces, Regularity theory
@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},
     publisher = {Elsevier},
     volume = {32},
     number = {4},
     year = {2015},
     pages = {901-924},
     doi = {10.1016/j.anihpc.2014.04.004},
     zbl = {1323.35216},
     mrnumber = {3390089},
     language = {en},
     url = {http://www.numdam.org/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, Volume 32 (2015) no. 4, pp. 901-924. doi : 10.1016/j.anihpc.2014.04.004. http://www.numdam.org/item/AIHPC_2015__32_4_901_0/

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