TY  - INPR
A1  - Mera, Azal
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The Neumann problem after Spencer
N2  - When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for
the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on
a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 6 
KW  - elliptic complex
KW  - manifold with boundary
KW  - Hodge theory
KW  - Neumann problem
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-90631
SN  - 2193-6943
VL  - 5
IS  - 6
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Harmonic integrals on domains with edges
N2  - We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.
T3  - Preprint - (2004) 20 
KW  - domains with singularities
KW  - de Rham complex
KW  - Neumann problem
KW  - Hodge theory
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26800
ER  -