The Dirichlet problem for the fractional Laplacian
tarafından
Alkın, Aykut, author.
Başlık
:
The Dirichlet problem for the fractional Laplacian
Yazar
:
Alkın, Aykut, author.
Yazar Ek Girişi
:
Alkın, Aykut, author.
Fiziksel Tanımlama
:
vi, 66 leaves:+ 1 computer laser optical disc.
Özet
:
This thesis is an introduction to the fractional Sobolev spaces and the fractional Laplace operator. We define the fractional Sobolev spaces and give their properties by comparing them with the classical version of Sobolev spaces. After giving the motivation that comes from the random walk theory, we define the fractional Laplacian. We focus on the mean-value property of s-harmonic functions and get into details of extension and maximum principle of the weak solution of the Dirichlet problem for the fractional Laplacian. Afterall, we explain the regularity of the weak solution of the Dirichlet problem for the fractional Laplacian inside a domain and up to the boundary, respectively.
Konu Başlığı
:
Differential equations, Partial.
Laplacian operator.
Fractional differential equations.
Dirichlet problem.
Yazar Ek Girişi
:
Özsarı, Türker,
Tüzel Kişi Ek Girişi
:
İzmir Institute of Technology. Mathematics.
Tek Biçim Eser Adı
:
Thesis (Master)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Master).
Elektronik Erişim
:
Library | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi |
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IYTE Library | Tez | T001686 | QA425 .A41 2017 | Tez Koleksiyonu |