5 papers · 1 filter
Generalized functions valued in a smooth manifold
Michael Kunzinger
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generali…
Generalized pseudo-Riemannian geometry
Michael Kunzinger, Roland Steinbauer
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving s…
Diffeomorphism invariant Colombeau algebras. Part III: Global theory
Michael Kunzinger
We present the construction of an associative, commutative algebra of generalized functions on a manifold satisfying the following optimal set of permanence…
Symmetry group analysis of weak solutions
N. Dapic, M. Kunzinger, S. Pilipovic
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following sett…
Foundations of a nonlinear distributional geometry
Michael Kunzinger, Roland Steinbauer
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tens…