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Strongly Elliptic Second Order Systems with Spectral Parameter in Transmission Conditions on a Nonclosed Surface

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Pseudo-Differential Operators and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 164))

Abstract

We consider a class of second order strongly elliptic systems in ℝn, n ≥ 3, outside a bounded nonclosed surface S with transmission conditions on S containing a spectral parameter. Assuming that S and its boundary γ are Lipschitz, we reduce the problems to spectral equations on S for operators of potential type. We prove the invertibility of these operators in suitable Sobolev type spaces and indicate spectral consequences. Simultaneously, we prove the unique solvability of the Dirichlet and Neumann problems with boundary data on S.

The work was supported by the grant of RFFI No. 04-01-00914.

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Author information

Authors and Affiliations

  1. Moscow Institute of Electronics and Mathematics (MIEM), Moscow, 109028, Russia

    M.S. Agranovich

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  1. M.S. Agranovich
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto, 10, 10123, Torino, Italy

    Paolo Boggiatto  & Luigi Rodino  & 

  2. School of Mathematics and Systems Engineering, Växjö University, SE-351 95, Växjö, Sweden

    Joachim Toft

  3. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Agranovich, M. (2006). Strongly Elliptic Second Order Systems with Spectral Parameter in Transmission Conditions on a Nonclosed Surface. In: Boggiatto, P., Rodino, L., Toft, J., Wong, M.W. (eds) Pseudo-Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 164. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7514-0_1

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