The Brezis-Nirenberg problem for the fractional Laplacian with mixed Dirichlet-Neumann boundary conditions

2018/05/25 by Colorado, Eduardo, Ortega, Alejandro · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.10093

Abstract

In this work we study the existence of solutions to the critical Brezis-Nirenberg problem when one deals with the spectral fractional Laplace operator and mixed Dirichlet-Neumann boundary conditions, i.e., \(-Δ)^su · amp; = · amp; λu+u^{2_s^*-1}, u · gt;0\quadin Ω,
u · amp; = · amp; 0\quadon Σ_D,
(∂ u)/(∂ ν) · amp; = · amp; 0\quadon Σ_N,. where Ω⊂ℝ^N is a regular bounded domain, (1)/(2)

Cited by

• Fractional critical systems with mixed boundary conditions
• Nonlocal critical problems with mixed boundary conditions and nearly resonant perturbations

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