Regularity results for quasilinear elliptic problems driven by the fractional Φ-Laplacian operator

2021/11/09 by Marcos L. M. Carvalho, Carvalho, M. L., E. D. Silva +5
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.05405

openalex publication_date 2021/11/09 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

Abstract

It is established L^p estimates for the fractional Φ-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 Φ-Laplacian operator defined in bounded domains belongs to L^∞(Ω) under appropriate hypotheses on the N-function Φ. 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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