Minimization of a fractional perimeter-Dirichlet integral functional

2013/06/22 by Luis Caffarelli, Ovidiu Savin, Caffarelli, Luis +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1306.5337

arxiv created 2013/06/22 · arxiv updated 2013/06/25

Abstract

We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely ∫_\Om |∇ u(x)|² dx+\Per(\u > 0\,\Om ), with σ∈(0,1). We obtain regularity results for the minimizers and for their free boundaries \p \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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