TY - JOUR
T1 - Minimization of a fractional perimeter-Dirichlet integral functional
AU - Caffarelli, Luis
AU - Savin, Ovidiu
AU - Valdinoci, Enrico
PY - 2015/7/1
Y1 - 2015/7/1
N2 - We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely (Formula presented.), 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.
AB - We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely (Formula presented.), 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.
KW - Fractional minimal surfaces
KW - Free boundary problems
KW - Regularity theory
UR - http://www.scopus.com/inward/record.url?scp=84940452256&partnerID=8YFLogxK
U2 - https://arxiv.org/pdf/1306.5337.pdf
DO - https://arxiv.org/pdf/1306.5337.pdf
M3 - Article
AN - SCOPUS:84940452256
SN - 0294-1449
VL - 32
SP - 901
EP - 924
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -