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On the $L^{\infty}$-regularity for fractional Orlicz problems via Moser’s iteration
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  • Marcos L. M. Carvalho,
  • Edcarlos Silva,
  • José Carlos de Albuquerque,
  • S. Bahrouni
Marcos L. M. Carvalho
Universidade Federal de Goias

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Edcarlos Silva
UFG
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José Carlos de Albuquerque
Universidade Federal de Pernambuco
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S. Bahrouni
University of Monastir
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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.
18 May 2022Submitted to Mathematical Methods in the Applied Sciences
19 May 2022Submission Checks Completed
19 May 2022Assigned to Editor
28 May 2022Reviewer(s) Assigned
02 Sep 2022Review(s) Completed, Editorial Evaluation Pending
06 Sep 2022Editorial Decision: Revise Minor
08 Sep 20221st Revision Received
09 Sep 2022Submission Checks Completed
09 Sep 2022Assigned to Editor
10 Sep 2022Review(s) Completed, Editorial Evaluation Pending
10 Sep 2022Editorial Decision: Accept
20 Oct 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8795