Equations involving fractional Laplacian operator: Compactness and application

2015/03/03 by Shusen Yan, Yan, Shusen, Jianfu Yang +3
Computer Science · Mathematics · #35J60 #35J65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1503.00788

openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the following problem involving fractional Laplacian operator: (-Δ)^α u= |u|^{2^*_α-2-ε}u + λu \rm in Ω, u=0 \rm on ∂Ω, where Ω is a smooth bounded domain in ℝ^N, ε∈ [0, 2^*_α-2), 06α and λ>0. An application of this compactness result is that problem \eqrefeq:0.1 possesses infinitely many solutions under the same assumptions.

Citations

• Regularity of the obstacle problem for a fractional power of the laplace operator
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

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