A fractional Hadamard formula and applications.

We consider the domain dependence of the best constant in the subcritical fractional Sobolev constant, $$ \lambda_{s,p}(\Omega):=\inf \left\{ [u]_{H^s(\mathbb{R}^N)}^2,\,\, u\in C^\infty_c(\Omega),\,\, \|u\|_{L^p(\Omega)}=1 \right\}, $$ where $s\in (0,1)$, $\Omega$ is bounded of class $C^{1,1}$ and $p\in [1, \frac{2N}{N-2s})$ if $2s

Keywords:

• Eigenvalues and eigenvectors
• Combinatorics
• Mathematics
• dirichlet laplacian
• Sobolev space
• Lambda
• Mathematical analysis
• Bounded function
• Hadamard transform
• Omega

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