Advances in Differential Equations

Asymptotic behaviour of the div-curl problem in exterior domains

Michael Neudert and Wolf von Wahl

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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

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

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Neudert, Michael; von Wahl, Wolf. Asymptotic behaviour of the div-curl problem in exterior domains. Adv. Differential Equations 6 (2001), no. 11, 1347--1376.

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