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Křížek, Michal; Neittaanmäki, Pekka

Solvability of a first order system in three-dimensional non-smooth domains. (English) Zbl 0593.35073

Apl. Mat. 30, 307-315 (1985).
The paper deals with solvability of the boundary value problem of magnetostatics in vacuum for a bounded domain with Lipschitz boundary. Existence and uniqueness results are well-known in the literature for more general anisotropic, inhomogeneous media (some of the related literature is quoted, however for other reasons). Nevertheless, the authors reconsider the problem, but seem to prefer a partly different approach. Trace theorems are employed to formulate boundary conditions that could more easily be formulated in the weak sense. Some results have been given a different proof. In the final result sufficient solvability conditions are missing, so that the use of the solvability statement is limited.
Reviewer: R.Picard

Cited in 3 Documents

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
78A30 Electro- and magnetostatics

Keywords:

Friedrich’s inequality; boundary value problem; magnetostatics in vacuum; bounded domain with Lipschitz boundary; Trace theorems
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Full Text: DOI EuDML

References:

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