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.
Minimization of a fractional perimeter-Dirichlet integral functional / L. Caffarelli, O. Savin, E. Valdinoci. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 32:4(2015), pp. 901-924. [10.1016/j.anihpc.2014.04.004]
Minimization of a fractional perimeter-Dirichlet integral functional
E. Valdinoci
2015
Abstract
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.
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