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Anglický jazyk
Besov spaces on fractals
Autor: Per Bylund
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,... Viac o knihe
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O knihe
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.
- Vydavateľstvo: LAP LAMBERT Academic Publishing
- Rok vydania: 2010
- Formát: Paperback
- Rozmer: 220 x 150 mm
- Jazyk: Anglický jazyk
- ISBN: 9783843369633
