Weighted  L   p  ‐theory for vector potential operators in three‐dimensional exterior domains | Zendy

Louati Hela | Zendy; Meslameni Mohamed | Zendy; Razafison Ulrich | Zendy

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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.

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