Nonhomogeneous boundary conditions for the spectral fractional Laplacian
| Autor: | Nicola Abatangelo, Louis Dupaigne |
|---|---|
| Přispěvatelé: | Abatangelo N., Dupaigne L., Université libre de Bruxelles (ULB), Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2017 |
| Předmět: |
Dirichlet problem
Large solution Applied Mathematics 010102 general mathematics Mathematical analysis Boundary (topology) Boundary blow-up solution 01 natural sciences Measure (mathematics) Domain (mathematical analysis) 010101 applied mathematics Mathematics - Analysis of PDEs Operator (computer programming) Harmonic function Spectral fractional Laplacian Bounded function FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Boundary value problem 0101 mathematics Mathematical Physics Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Annales de l'Institut Henri Poincaré (C) Non Linear Analysis Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2016, ⟨10.1016/j.anihpc.2016.02.001⟩ |
| ISSN: | 1873-1430 0294-1449 |
| DOI: | 10.1016/j.anihpc.2016.02.001 |
| Popis: | We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value problems associated with nonhomogeneous boundary conditions. We provide a weak-$L^1$ theory to show how problems with measure data at the boundary and inside the domain are well-posed. We study linear and semilinear problems, performing a sub- and supersolution method, and we finally show the existence of large solutions for some power-like nonlinearities. Comment: 26 pages |
| Databáze: | OpenAIRE |
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