WIAS Preprint No. 1818, (2013)
Minimization of a fractional perimeter-Dirichlet integral functional
Authors
- Caffarelli, Luis
- Savin, Ovidiu
- Valdinoci, Enrico
ORCID: 0000-0001-6222-2272
2010 Mathematics Subject Classification
- 35B65 49Q05 31A05 49Q15
Keywords
- regularity results, free boundary problems, monotonicity formulas
DOI
Abstract
We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set. We obtain regularity results for the minimizers and for their free boundaries using blow-up analysis, density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.
Download Documents