12-41 Raffaella Servadei and Enrico Valdinoci
A Brezis-Nirenberg result for non-local critical equations in low dimension (68K, LaTeX) Apr 25, 12
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Abstract. The present paper is devoted to the study of the following non-local fractional equation involving critical nonlinearities $$\left\{ egin{array}{ll} (-\Delta)^s u-\lambda u=|u|^{2^*-2}u & {\mbox{ in }} \Omega\ u=0 & {\mbox{ in }} \RR^n\setminus \Omega\,, \end{array} ight.$$ where $s\in (0,1)$ is fixed, $(-\Delta )^s$ is the fractional Laplace operator, $\lambda$ is a positive parameter, $2^*$ is the fractional critical Sobolev exponent and $\Omega$ is an open bounded subset of $\RR^n$, $n\in(2s,4s)$\,, with Lipschitz boundary.

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