Raffaella Servadei and Enrico Valdinoci
Lewy-Stampacchia type estimates for variational 
inequalities driven by (non)local operators
(98K, LaTex)

ABSTRACT.  The purpose of this paper is to derive some Lewy-Stampacchia 
estimates in some cases of interest, such as the ones driven by 
non-local operators. Since we will perform an abstract approach to 
the problem, this will provide, as a byproduct, Lewy-Stampacchia 
estimates in more classical cases as well. In particular, we can 
recover the known estimates for the standard Laplacian, the 
$p$-Laplacian, and the Laplacian in the Heisenberg group. In the 
non-local framework we prove a Lewy-Stampacchia estimate for a 
general integrodifferential operator and, as a particular case, 
for the fractional Laplacian. As far as we 
know, the results in the non-local setting are new.