The Brezis-Nirenberg problem for the fractional p-Laplacian involving critical Hardy-Sobolev exponents

2017/10/12 by Yang Yang, Yang, Yang
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.1710.04654

openalex publication_date 2017/10/12 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

We obtain existence, multiplicity, and bifurcation results for the Brezis-Nirenberg problem for the fractional p\nobreakdash-Laplacian operator, involving critical Hardy-Sobolev exponents. Our results are mainly extend results in the literature for α=0. In the absence of an explicit formula for a minimizer in the fractional Hardy-Sobolev inequality α\not= 0, we get around this difficulty by working with certain asymptotic estimates for minimizers recently obtained in \citeMM.

Citations

• Fractional p-eigenvalues
• Nonlocal Harnack inequalities
• The Brezis-Nirenberg result for the fractional Laplacian
• A relation between pointwise convergence of functions and convergence of functionals
• p-Laplacian problems involving critical Hardy-Sobolev exponents

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• Brezis-Nirenberg type problem for fractional sub-Laplacian on the Heisenberg group
• Existence of Positive Solutions for Generalized Fractional Brézis-Nirenberg Problem
• The Brezis-Nirenberg problem for the fractional Laplacian with mixed Dirichlet-Neumann boundary conditions
• The Brezis-Nirenberg Result for the Fractional Elliptic Problem with Singular Potential