2018/01/01 by Jesús Ildefonso Díaz Díaz, Jesús Ildefonso Díaz, David Gómez-Castro +6 · 31 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary (topology) #Boundary value problem #Bounded function #Class (philosophy) #Differential Equations and Boundary Problems #Dirichlet boundary condition #Dirichlet distribution #Dirichlet problem #Domain (mathematical analysis) #Fractional Laplacian #Integrable system #Laplace operator #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Omega #Physics #Pure mathematics #Quantum mechanics #Schrödinger equation #Space (punctuation) #math.AP #msc:35D30 #msc:35J10 #msc:35J67 #msc:35J75
paper · pdf · doi:10.1016/j.na.2018.05.001
published in arXiv (Cornell University) 177, 325-360 (Cornell University)
openalex publication_date 2018/01/01 · arxiv created 2018/05/11 · openalex created_date 2019/07/30 · arxiv updated 2022/02/23 · openalex updated_date 2026/08/05
We study the Dirichlet problem for the stationary Schrödinger fractional Laplacian equation (-Δ)s u + V u = f posed in bounded domain Ω⊂ \mathbb Rn with zero outside conditions. We consider general nonnegative potentials V∈ L1loc(Ω) and prove well-posedness of very weak solutions when the data are chosen in an optimal class of weighted integrable functions f. Important properties of the solutions, such as its boundary behaviour, are derived. The case of super singular potentials that blow up near the boundary is given special consideration. Related literature is commented.