GROUND STATE SOLUTIONS FOR A CRITICAL FRACTIONAL LAPLACIAN EQUATION IN UNBOUNDED DOMAINS: EXISTENCE AND REGULARITY

In this work we study the following fractional critical problem {(-triangle)(s)u=lambda|u|(q-2)u+|u|2(s)(& lowast;)-(2)u in ohm, u= 0 in R-N\ohm, where ohm is an open unbounded strip-like domain in R-N,N >2s with s is an element of(0,1),lambda >0,q is an element of[2,2(s)(& lowast;)-) and 2(s)(& lowast;)= 2(N)/(N-2s). By variational methods, we prove the existence of positive ground state solutions to theproblem. Further, we study the regularity of these solutions. Precisely,using a Brezis-Kato type estimate for unbounded domains, we establish the L-infinity-bound on nonnegative solutions of the equation for certain range of q. The present work extends the existence and regularity results for fractional Laplace equations to unbounded domains