Geodesic
Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 1-15

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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 $H^s$, the simplest $L_2$-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.
Keywords: strong ellipticity, Lipschitz domain, nonclosed boundary, potential type operators, Bessel potential spaces, regularity of solutions, spectral transmission problems, spectral asymptotics.
Mots-clés : Besov spaces 
@article{FAA_2011_45_1_a0,
     author = {M. S. Agranovich},
     title = {Strongly {Elliptic} {Second-Order} {Systems} with {Boundary} {Conditions} on a {Nonclosed} {Lipschitz} {Surface}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {1--15},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a0/}
}
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M. S. Agranovich. Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a0/