41 research outputs found
Diffeomorphic approximation of Sobolev homeomorphisms
Every homeomorphism h : X -> Y between planar open sets that belongs to the
Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm
by diffeomorphisms.Comment: 21 pages, 5 figure
Algebrability and nowhere Gevrey differentiability
We show that there exist c-generated algebras (and dense in C^infty([0,1])) every
nonzero element of which is a nowhere Gevrey diff erentiable function. This leads to results
of dense algebrability (and, therefore, lineability) of functions enjoying this property. In
the process of proving these results we also provide a new construction of nowhere Gevrey
di fferentiable functions