Mixed problems in a Lipschitz domain for strongly elliptic second-order systems

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Abstract

We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space ℝ n . For such problems, equivalent equations on the boundary in the simplest L 2-spaces H s of Sobolev type are derived, which permits one to represent the solutions via surface potentials. We prove a result on the regularity of solutions in the slightly more general spaces H p s of Bessel potentials and Besov spaces B p s . Problems with spectral parameter in the system or in the condition on a part of the boundary are considered, and the spectral properties of the corresponding operators, including the eigenvalue asymptotics, are discussed.

Key words

strongly elliptic system mixed problem potential type operator spectral problem eigenvalue asymptotics 
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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Moscow Institute of Electronics and MathematicsMoscowRussia

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