 1240 Raffaella Servadei
 The Yamabe equation in a nonlocal setting
(85K, LaTeX)
Apr 25, 12

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. Aim of this paper is to study the following elliptic equation driven by a general nonlocal integrodifferential operator~$\mathcal L_K$
$$\left\{
egin{array}{ll}
\mathcal L_K u+\lambda u+u^{2^*2}u=0 & \mbox{in } \Omega\
u=0 & \mbox{in } \RR^n\setminus \Omega\,,
\end{array}
ight.$$
where $s\in (0,1)$, $\Omega$ is an open bounded set of $\RR^n$, $n>2s$, with Lipschitz boundary, $\lambda$ is a positive real parameter, $2^*=2n/(n2s)$ is a fractional critical Sobolev exponent, while $\mathcal L_K$ is the nonlocal integrodifferential operator
$$\mathcal L_Ku(x)=
rac12
\int_{\RR^n}\Big(u(x+y)+u(xy)2u(x)\Big)K(y)\,dy\,,
\,\,\,\,\, x\in \RR^n\,.$$
As a concrete example, we consider the case when $K(x)=x^{(n+2s)}$\,, which gives rise to the fractional Laplace operator $(\Delta)^s$\,.
 Files:
1240.src(
1240.keywords ,
servadeiY120425.tex )