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On solvability of elliptic boundary value problems via global invertibility

Bełdziński Michał, Galewski Marek

Opuscula Mathematica

2020

Vol. 40, no. 1

37--47

In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions.

On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative

Bełdziński Michał, Galewski Marek

Opuscula Mathematica

2019

Vol. 39, no. 2

131-144

In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.

Commutators of diffeomorphisms of a manifold with corners

Lech J.

Demonstratio Mathematica

2007

Vol. 40, nr 2

465-480

It is shown that the identity component of the group of al compac tly suported C infinity -diffeomorphisms of a manifold with corners is perfect provided the manifold has no vertices. An analogous result for Cr -diffeomorphism still holds whenever r > n+1, wheren is the dimension of the manifold. These results constiute a generalization of a well-known theorem by Thurston and Mather on the simplicity of diffeomorphism groups of boundaryless manifolds.

Euler-Poincare formalism of coupled KdV type system and diffeomorphism group on S1

Guha P.

Journal of Applied Analysis

2005

Vol. 11, nr 2

261-282

This paper describes a wide class of coupled KdV equations. The first set of equations directly follow from the geodesic flows on the Bott-Virasoro group with a complex field. But the set of 2-component systems of nonlinear evolution equations, which includes dispersive water waves, Ito's equation, many other known and unknown equations, follow from the geodesic flows of the right invariant L2 metric on the semidirect product group [wzór], where Diff(S1) is the group of orientation preserving diffeomorphisms on a circle. We compute the Lie-Poisson brackets of the Antonowicz-Fordy system, and the mode expansion of these beackets yield the twisted Heisenberg-Virasoro algebra. We also give an outline to study geodesic flows of a H1 metric on [wzór].