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

We study the existence of weak solutions to $ p $-Navier-Stokes equations with a symmetric $-Laplacian on bounded domains. construct particular Schauder basis in W_0^{1,p}(\Omega) divergence free constraint and prove using Galerkin approximation via this basis. Meanwhile, proof, we establish chain rule for L^p integral solutions, which fixes gap our previous work. The equality energy dissipatio...