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arXiv · 1306.5337

Minimization of a fractional perimeter-Dirichlet integral functional

Luis Caffarelli·Ovidiu Savin·Enrico Valdinoci
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Abstract

We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely $$ \int_\Om |\nabla u(x)|^2\,dx+\Per\Big(\{u > 0\},\Om \Big),$$ with $\sigma\in(0,1)$. 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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Luis Caffarelli, Ovidiu Savin, Enrico Valdinoci. 2013-06-22. Minimization of a fractional perimeter-Dirichlet integral functional. https://arxiv.org/abs/1306.5337

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