Advances in Differential Equations

Asymptotic behaviour of the div-curl problem in exterior domains

Michael Neudert and Wolf von Wahl

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Abstract

We study the variety of solutions of the inhomogeneous div--curl problem in exterior domains in dependence on the decay conditions on div and curl. Here we consider the Neumann as well as the Dirichlet boundary value prescription where in the first case the topological impact is decisive. In the second case the integrability conditions on div, curl and the boundary values are more difficult. Finally we present Hölder estimates for the solution of the Dirichlet or Neumann problem where it is unique.

Article information

Source
Adv. Differential Equations Volume 6, Number 11 (2001), 1347-1376.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357139964

Mathematical Reviews number (MathSciNet)
MR1859351

Zentralblatt MATH identifier
1016.35068

Subjects
Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35F15: Boundary value problems for linear first-order equations 78A30: Electro- and magnetostatics

Citation

Neudert, Michael; von Wahl, Wolf. Asymptotic behaviour of the div-curl problem in exterior domains. Adv. Differential Equations 6 (2001), no. 11, 1347--1376. https://projecteuclid.org/euclid.ade/1357139964.


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