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dc.contributor.authorKimaczyńska, Anna
dc.date.accessioned2017-07-04T06:07:57Z
dc.date.available2017-07-04T06:07:57Z
dc.date.issued2016-06-08
dc.identifier.urihttp://hdl.handle.net/11089/22071
dc.description.abstractDifferential operators: the gradient grad and the divergence div are defined and examined in the bundles of symmetric tensors on a Riemannian manifold. For the second order operator div grad which appears to be elliptic and a manifold with boundary a system of natural boundary conditions is constructed and investigated. There are 2k+1 conditions in the bundle Sk of symmetric tensors of degree k. This is in contrast to the bundle of skewsymmetric forms where (for analogous differential operators) there are always four such conditions independently of the degree of forms (i.e. independently of k). All the 2k+1 conditions are investigated in detail. In particular, it is proved that each of them is self-adjoint and elliptic. Such the ellipticity of a given boundary condition has an essential significance for the existing of an orthonormal basis in L2 consisting of smooth sections that are the eigenvalues of the operator and satisfy the boundary condition. Some special cases, e.g. k = 1 or the the cases that the boundary is umbilical or totally geodesic are also discussed.pl_PL
dc.language.isoenpl_PL
dc.subjectSymmetric tensorspl_PL
dc.subjectgradientpl_PL
dc.subjectdivergencepl_PL
dc.subjectElliptic operatorspl_PL
dc.subjectElliptic boundary conditionspl_PL
dc.subjectWeitzenboeck type formulapl_PL
dc.titleThe differential operators in the bundle of symmetric tensors on a Riemannian manifoldpl_PL
dc.typePhD/Doctoral Dissertationpl_PL
dc.rights.holderAnna Kimaczyńskapl_PL
dc.page.number59pl_PL
dc.contributor.authorAffiliationFaculty of Mathematics and Computer Science, The Lodz Universitypl_PL
dc.contributor.authorEmailkimaczynska@math.uni.lodz.plpl_PL
dc.dissertation.directorPierzchalski, Antoni
dc.dissertation.reviewerOrsted, Bent
dc.dissertation.reviewerIzydorek, Marek
dc.date.defence2017-07-05


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