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Besov spaces on fractals: Trace theorems and measures on arbitrary closed subsets of n-space

A physical state in a domain is often described by a model containing a linear partial differential equation. As an example of this, consider the steady state temperature distribution in a homogenous isotropic body. The problem, called Dirichlet’s problem, is to find a function u, given that ?u=f in the interior of the body and u=g on the surface (where ?u denotes the laplacian of u). The solution depends on f and g, but also on the geometry of the surface S. If the given functions f and g, as well as the subset S of 3-space, are smooth enough, then there exists a unique solution. However, since there are numerous non-smooth structures in nature, it is clear that the study of Dirichlet’s problem in the case when f, g and S are less smooth becomes an important task. Function spaces defined on subsets of n-space originates from the study of Dirichlet’s problem in the non-smooth case of f, g and S. An important class of functions in this respect are Besov spaces, defined in n-space in the 60’s. In the 80’s Besov spaces were extended to d-sets, typically fractal sets with non-integer local dimension d. In this book we extend Besov space theory to sets with varying local dimension.

Author: Per Bylund

Binding: Paperback

EAN: 9783843369633

Condition: New

Manufacturer: LAP LAMBERT Academic Publishing

Number of items: 1

Number of pages: 124

Product group: Book

Studio: LAP LAMBERT Academic Publishing

Publication Date: 2010-10-29

Publisher: LAP LAMBERT Academic Publishing

Pages: 124

ISBN: 3843369631

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Per Bylund
Contact Per BylundTwitter AwardsLawrence W. Fertig Prize in Austrian Economics Per L. Bylund, PhD, is Assistant Professor of Entrepreneurship and Records-Johnston Professor of Free Enterprise in the School of Entrepreneurship at Oklahoma State University. Visit his website at PerBylund.com.