TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Pseudodifferential subspaces and their applications in elliptic theory
N2  - The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah–Patodi–Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.
T3  - Preprint - (2005) 17 
KW  - elliptic operator
KW  - boundary value problem
KW  - pseudodifferential subspace
KW  - dimension functional
KW  - η-invariant
KW  - index
KW  - modn-index
KW  - parity condition
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29937
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Index defects in the theory of nonlocal boundary value problems and the η-invariant
N2  - The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities.
T3  - Preprint - (2001) 31 
KW  - elliptic operator
KW  - boundary value problem
KW  - finiteness theorem
KW  - nonlocal problem
KW  - covering
KW  - relative η-invariant
KW  - index
KW  - modn-index
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26146
ER  - 
TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Normally solvable nonlinear boundary value problems
N2  - We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)11 
KW  - Nonlinear Laplace operator
KW  - boundary value problem
KW  - Dirichlet to Neumann operator
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-65077
SN  - 2193-6943
ER  -