On the embedding constant of the Sobolev type inequality for fractional derivatives

• Mizuguchi Makoto

  Graduate School of Fundamental Science and Engineering, Waseda University

• Takayasu Akitoshi

  Research Institute for Science and Engineering, Waseda University

• Kubo Takayuki

  Institute of Mathematics, University of Tsukuba

• Oishi Shin'ichi

  Department of Applied Mathematics, Faculty of Science and Engineering, Waseda University CREST, JST

抄録

This paper is concerned with the embedding constant of the Sobolev type inequality for fractional derivatives on $\Omega\subset\mathbb{R}^{N}~(N\in\mathbb{N})$. The constant is explicitly described using the analytic semigroup over L²(Ω) generated by the Laplace operator. Some numerical examples of estimating the embedding constant are also provided.

収録刊行物

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 7 (3), 386-394, 2016

  一般社団法人 電子情報通信学会

キーワード

• embedding constant
• Sobolev inequality
• fractional derivative
• analytic semigroup

詳細情報

• CRID: 1390282680323519104
• NII論文ID: 130005161829
• DOI: 10.1587/nolta.7.386
• ISSN: 21854106
• HANDLE: 2241/00146058
• Web Site: https://tsukuba.repo.nii.ac.jp/records/41110
• Web Site: https://www.jstage.jst.go.jp/article/nolta/7/3/7_386/_pdf
• 本文言語コード: en
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