 1241 Raffaella Servadei and Enrico Valdinoci
 A BrezisNirenberg result
for nonlocal 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 nonlocal 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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