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arXiv · 2111.05405

Regularity results for quasilinear elliptic problems driven by the fractional $\Phi$-Laplacian operator

M. L. Carvalho·E. D. Silva·J. C. de Albuquerque·S. Bahrouni
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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.

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M. L. Carvalho, E. D. Silva, J. C. de Albuquerque, S. Bahrouni. 2021-11-09. Regularity results for quasilinear elliptic problems driven by the fractional $\Phi$-Laplacian operator. https://arxiv.org/abs/2111.05405

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