Abstract:
An operator algebra associated with a smooth embedding i:X↪M is constructed. For elliptic elements of this algebra a finiteness theorem (the Fredholm property) is established, and the index is computed. A connection with Sobolev problems is shown.
\Bibitem{SteSha96}
\by B.~Yu.~Sternin, V.~E.~Shatalov
\paper Relative elliptic theory and the~Sobolev problem
\jour Sb. Math.
\yr 1996
\vol 187
\issue 11
\pages 1691--1720
\mathnet{http://mi.mathnet.ru/eng/sm174}
\crossref{https://doi.org/10.1070/SM1996v187n11ABEH000174}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1438986}
\zmath{https://zbmath.org/?q=an:0882.58053}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996WQ48500005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0030299673}
Linking options:
https://www.mathnet.ru/eng/sm174
https://doi.org/10.1070/SM1996v187n11ABEH000174
https://www.mathnet.ru/eng/sm/v187/i11/p115
This publication is cited in the following 15 articles:
Anton Savin, “The Friedrichs Extension of Elliptic Operators with Conditions on Submanifolds of Arbitrary Dimension”, Mathematics, 12:3 (2024), 418
D. A. Poluektova, A. Yu. Savin, B. Yu. Sternin, “On the Algebra of Operators Corresponding to the Union of Smooth Submanifolds”, J Math Sci, 265:5 (2022), 839
N. R. Izvarina, A. Yu. Savin, “Complexes in relative elliptic theory”, Eurasian Math. J., 11:4 (2020), 45–57
Sipailo P.A., “Traces of Quantized Canonical Transformations on Submanifolds and Their Applications to Sobolev Problems With Nonlocal Conditions”, Russ. J. Math. Phys., 26:1 (2019), 135–138
D. A. Poluektova, A. Yu. Savin, B. Yu. Sternin, “Ob algebre operatorov, otvechayuschei ob'edineniyu gladkikh podmnogoobrazii”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 672–682
P. A. Sipailo, “On Traces of Fourier Integral Operators on Submanifolds”, Math. Notes, 104:4 (2018), 559–571
Loshchenova D.A., “Sobolev Problems Associated With Lie Group Actions”, Differ. Equ., 51:8 (2015), 1051–1064
A. Yu. Savin, B. Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Dokl. Math, 89:1 (2014), 61
Yu. A. Kordyukov, V. A. Pavlenko, “Singular integral operators on a manifold with a distinguished submanifold”, Ufa Math. J., 6:3 (2014), 35–68
Savin A.Yu., Sternin B.Yu., “Index of Sobolev Problems on Manifolds With Many-Dimensional Singularities”, Differ. Equ., 50:2 (2014), 232–245
Nguen L.L., “Zadachi soboleva dlya deistvii konechnykh grupp”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 125–133
Sobolev problems for finite group actions
Korovina, MV, “Relative elliptic morphisms and some of their applications”, Doklady Mathematics, 77:2 (2008), 226
Korovina, MV, “Relative elliptic operators and the Sobolev problem: II”, Differential Equations, 43:4 (2007), 525
Vladimir Nazaikinskii, Boris Sternin, Aspects of Boundary Problems in Analysis and Geometry, 2004, 495
Nazaikinskii, VE, “On the Green operator in relative elliptic theory”, Doklady Mathematics, 68:1 (2003), 57
Citation in format AMSBIB
Contact us: