Displaying similar documents to “Natural transformations of foliations into foliations on the cotangent bundle”

Liftings of 1 -forms to the linear r -tangent bundle

Włodzimierz M. Mikulski (1995)

Archivum Mathematicum

Similarity:

Let r , n be fixed natural numbers. We prove that for n -manifolds the set of all linear natural operators T * → T * T ( r ) is a finitely dimensional vector space over R . We construct explicitly the bases of the vector spaces. As a corollary we find all linear natural operators T * → T r * .

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

Similarity:

Let Ω be a bounded open subset of ℝ n , n > 2 . In Ω we deduce the global differentiability result u ∈ H 2 ( Ω , ℝ N ) for the solutions u ∈ H 1 ( Ω , ℝ n ) of the Dirichlet problem u - g ∈ H 0 1 ( Ω , ℝ N ) , - ∑ i D i a i ( x , u , D u ) = B 0 ( x , u , D u ) with controlled growth and nonlinearity q = 2 . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.