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Besov spaces on fractals

Besov spaces on fractals


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About the Book

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.


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Product Details
  • ISBN-13: 9783843369633
  • Publisher: Lap Lambert Academic Publishing
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 7 mm
  • Width: 152 mm
  • ISBN-10: 3843369631
  • Publisher Date: 29 Oct 2010
  • Height: 229 mm
  • No of Pages: 124
  • Series Title: English
  • Weight: 240 gr


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