Besov spaces on fractals - Bylund, Per
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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…mehr

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Produktbeschreibung
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 inthe 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.
Autorenporträt
Per Bylund, PhD in mathematics. Assistant professor at university of Umeå, Sweden. Research area: function spaces and measures.