  In this paper we study an elliptic variational problem regarding the
$p$-fractional Laplacian in $\mathbb{R}^N$ on the basis of recent result
\cite{Ha1}, which generalizes the nice work \cite{AT,AP,XZR1}, and then give
some sufficient conditions under which some weak solutions to the above
elliptic variational problem are continuous in $\mathbb{R}^N$. In the final
appendix we correct the proofs of both \cite[Lemma 10]{PXZ1} and \cite[Lemma
A.6]{PXZ} for $1<p<2$.
