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Publicação
The fractal Dirichlet Laplacian
Autores
Orientador(es)
Resumo(s)
An h-set is a non-empty compact subset of the Euclidean n-space which supports a finite Radon measure for which the measure of balls centered on the subset is essentially given by the image of their radius by a suitable function h. In most cases of interest such a subset has Lebesgue measure zero and has a fractal structure.
We prove the existence of solutions for the so-called fractal Dirichlet problem for such h-sets.
The “construction” of the solutions is based on the consideration of complete o.n. systems for convenient function spaces on the fractals. These systems are obtained combining properties of traces with integral representations (obtained with the help of Green’s functions) for the so-called fractal Laplacian.
Descrição
Palavras-chave
Traces h-sets · Laplacian · Dirichlet problem · Function spaces · Fractals ·
Contexto Educativo
Citação
Caetano, A.M., Lopes, S. The fractal Dirichlet Laplacian. Rev Mat Complut 24, 189–209 (2011). https://doi.org/10.1007/s13163-010-0035-6
Editora
Springer Science and Business Media LLC