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Solvability of a first order system in three-dimensional non-smooth domains

Michal Křížek, Pekka Neittaanmäki (1985)

Aplikace matematiky

A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain Ω ⊂ 𝐑 3 . On the boundary δ Ω , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

Static electromagnetic fields in monotone media

Rainer Picard (1992)

Banach Center Publications

The paper considers the static Maxwell system for a Lipschitz domain with perfectly conducting boundary. Electric and magnetic permeability ε and μ are allowed to be monotone and Lipschitz continuous functions of the electromagnetic field. The existence theory is developed in the framework of the theory of monotone operators.

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