Existence and regularity of solutions for a class of fractional Laplacian problems.

In this paper, we first establish a modified Marcinkiewicz interpolation result, and using this result, we obtain a new regularity result for a fractional Laplacian problem on a bounded C 1 , 1 -domain Ω in R N , and we also obtain a new regularity result for then fractional problem on unbounded Ω = R N by using the Stampacchia truncation method. Next, by the Leray-Schauder fixed point theorem we obtain the existence of solutions for a class of fractional Laplacian problems with weak growth conditions on the nonlinearities. Finally, as an application, we prove the existence of positive solutions for a fractional Laplacian problem which has an exponential growth nonlinearity. [ABSTRACT FROM AUTHOR]