Now showing items 11-13 of 13
Navier-Stokes Equations for Elliptic Complexes
(Сибирский федеральный университет. Siberian Federal University, 2019-02)
We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam´e system, on manifold with boundary. To this end we interpret them in terms of the de ...
The de Rham Cohomology through Hilbert Space Methods
(Сибирский федеральный университет. Siberian Federal University, 2019-08)
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 ...
A Degree Theory for Lagrangian Boundary Value Problems
(Сибирский федеральный университет. Siberian Federal University, 2020-02)
We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian ...