Semilinear Dirichlet problem for subordinate spectral Laplacian

2022/06/17 by Ivan Biocic, Biocic, Ivan
Computer Science · Mathematics · #31B10 #31B25 #31C05 #35R11 #60J35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J61 #Probability (math.PR) #Secondary 35C15 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.08552

openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study semilinear problems in bounded C^1,1 domains for non-local operators with a boundary condition. The operators cover and extend the case of the spectral fractional Laplacian. We also study harmonic functions with respect to the non-local operator and boundary behaviour of Green and Poisson potentials.

Related

• Large solutions for subordinate spectral Laplacian
• Nonhomogeneous boundary conditions for the spectral fractional Laplacian
• Semilinear equations for non-local operators: beyond the fractional Laplacian
• Large solutions to semilinear equations for subordinate Laplacians in C^1,1 bounded open sets
• Mixed local and nonlocal Dirichlet (p,q)-eigenvalue problem