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Weighted L p ‐theory for vector potential operators in three‐dimensional exterior domains
Author(s) -
Louati Hela,
Meslameni Mohamed,
Razafison Ulrich
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3615
Subject(s) - mathematics , sobolev space , dirichlet distribution , helmholtz equation , laplace's equation , potential theory , vector valued function , neumann boundary condition , pure mathematics , mathematical analysis , order (exchange) , boundary (topology) , infinity , laplace transform , dirichlet problem , boundary value problem , finance , economics
In the present paper, we study the vector potential problem in exterior domains ofR 3 . Our approach is based on the use of weighted spaces in order to describe the behavior of functions at infinity. As a first step of the investigation, we prove important results on the Laplace equation in exterior domains with Dirichlet or Neumann boundary conditions. As a consequence of the obtained results on the vector potential problem, we establish useful results on weighted Sobolev inequalities and Helmholtz decompositions of weighted spaces. Copyright © 2015 John Wiley & Sons, Ltd.