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Public Documents
1
On the $L^{\infty}$-regularity for fractional Orlicz problems via Moser’s iteration
Marcos L. M. Carvalho
and 3 more
May 19, 2022
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.