On the $L^{\infty}$-regularity for fractional
Orlicz problems via Moser’s iteration
Abstract
It is established $L^{p}$ estimates for the fractional
$\Phi$-Laplacian operator defined in bounded domains
where the nonlinearity is subcritical or critical in a suitable sense.
Furthermore, using some fine estimates together with the Moser’s
iteration, we prove that any weak solution for fractional
$\Phi$-Laplacian operator defined in bounded domains
belongs to $L^\infty(\Omega)$ under
appropriate hypotheses on the $N$-function $\Phi$.
Using the Orlicz space and taking into account the fractional setting
for our problem the main results are stated for a huge class of
nonlinear operators and nonlinearities.