On the L ∞ ‐regularity for fractional Orlicz problems via Moser's iteration
Marcos L. M. Carvalho, Edcarlos D. Silva, José Carlos de Albuquerque, Sabri Bahrouni
Source abstract
estimates for the fractional ‐Laplacian operator defined in bounded domains are established, where the nonlinearity is subcritical or critical in a suitable sense. Furthermore, using some fine estimates together with Moser's iteration, we prove that any weak solution for fractional ‐Laplacian operator defined in bounded domains belongs to , under appropriate hypotheses on the ‐function . 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.
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