TY  - JOUR
A1  - Malass, Ihsane
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The de Rham Cohomology through Hilbert Space Methods
T2  - Journal of Siberian Federal University. Mathematics & physics
N2  - We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler-Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer.
KW  - De Rham complex
KW  - cohomology
KW  - Hodge theory
KW  - Neumann problem
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/50627
SN  - 1997-1397
SN  - 2313-6022
VL  - 12
IS  - 4
SP  - 455
EP  - 465
PB  - Sibirskij Federalʹnyj Universitet
CY  - Krasnoyarsk
ER  -