Hölder-Zygmund regularity in algebras of generalized functions

Details Hölder-Zygmund regularity in algebras of generalized functions Hölder-Zygmund regularity in algebras of generalized functions

2001-12-20

arxiv.org/abs/math/0112222v6

Mathematics

Analysis of PDEs

Scientific paper

We introduce an intrinsic notion of Hoelder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hoelder space this is shown to be consistent. The definition is motivated by the well-known use of Littlewood-Paley decomposition in characterizing Hoelder-Zygmund regularity for distributions. It is based on a simple interplay of differentiated convolution-mollification with wavelet transforms, which directly translates wavelet estimates into properties of the regularizations. Thus we obtain a scale of new subspaces of the Colombeau algebra. We investigate their basic properties and indicate first applications to differential equations whose coefficients are non-smooth but belong to some Hoelder-Zygmund class (distributional or generalized). In applications problems of this kind occur, for example, in seismology when Earth's geological properties of fractal nature have to be taken into account while the initial data typically involve strong singularities.

Affiliated with

Also associated with

No associations

Rating

Hölder-Zygmund regularity in algebras of generalized functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hölder-Zygmund regularity in algebras of generalized functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hölder-Zygmund regularity in algebras of generalized functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-314897