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October 19, 2026
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Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface

Functional Analysis and Its Applications. 2011. Vol. 45. No. 1. P. 1–12.
Agranovich M. S.

We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface S with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces Hs , the simplest L2-spaces of the Sobolev type, with the use of potential type operators on S. We also discuss, first, the regularity of solutions in somewhat more general Bessel potential spaces and Besov spaces and, second, the spectral properties of problems with spectral parameter in the transmission conditions on S, including the asymptotics of the eigenvalues.

Priority areas: mathematics
Language: English
Full text
Keywords: сильно эллиптическая системалипшицева областьнезамкнутая границаграничные задачизадачи сопряженияоператоры типа потенциалаstrongly elliptic systemLipschitz domainnonclosed boundaryboundary value problemstransmission problemspotential type operatorsBessel potential spacesBesov spacesregularity of solutionsspectral transmission problemsspectral asymptoticsпространства бесселевых потенциаловпространства Бесоварегулярность решенийспектральные задачи сопряженияспектральные асимптотики
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