The semigroup generated by the Dirichlet Laplacian of fractional order

Tsukasa Iwabuchi

doi:10.2140/apde.2018.11.683

The semigroup generated by the Dirichlet Laplacian of fractional order

Tsukasa Iwabuchi

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In the whole space ℝ^d, linear estimates for heat semigroup in Besov spaces are well established, which are estimates of L^p-L^q type, with maximal regularity, etc. This paper is concerned with such estimates for the semigroup generated by the Dirichlet Laplacian of fractional order in terms of the Besov spaces on an arbitrary open set of ℝ^d.

Original language	English
Pages (from-to)	683-703
Number of pages	21
Journal	Analysis and PDE
Volume	11
Issue number	3
DOIs	https://doi.org/10.2140/apde.2018.11.683
Publication status	Published - 2018

Keywords

Besov spaces
Dirichlet Laplacian
Semigroup

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2018.11.683

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abstract = "In the whole space ℝd, linear estimates for heat semigroup in Besov spaces are well established, which are estimates of Lp-Lq type, with maximal regularity, etc. This paper is concerned with such estimates for the semigroup generated by the Dirichlet Laplacian of fractional order in terms of the Besov spaces on an arbitrary open set of ℝd.",

keywords = "Besov spaces, Dirichlet Laplacian, Semigroup",

author = "Tsukasa Iwabuchi",

note = "Funding Information: The author would like to thank the referee for his important comments. The author was supported by the Grant-in-Aid for Young Scientists (B) (No. 25800069) from JSPS and by the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers. Publisher Copyright: {\textcopyright} 2018 Mathematical Sciences Publishers.",

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N1 - Funding Information: The author would like to thank the referee for his important comments. The author was supported by the Grant-in-Aid for Young Scientists (B) (No. 25800069) from JSPS and by the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers. Publisher Copyright: © 2018 Mathematical Sciences Publishers.

PY - 2018

Y1 - 2018

N2 - In the whole space ℝd, linear estimates for heat semigroup in Besov spaces are well established, which are estimates of Lp-Lq type, with maximal regularity, etc. This paper is concerned with such estimates for the semigroup generated by the Dirichlet Laplacian of fractional order in terms of the Besov spaces on an arbitrary open set of ℝd.

AB - In the whole space ℝd, linear estimates for heat semigroup in Besov spaces are well established, which are estimates of Lp-Lq type, with maximal regularity, etc. This paper is concerned with such estimates for the semigroup generated by the Dirichlet Laplacian of fractional order in terms of the Besov spaces on an arbitrary open set of ℝd.

KW - Besov spaces

KW - Dirichlet Laplacian

KW - Semigroup

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ER -

The semigroup generated by the Dirichlet Laplacian of fractional order

Abstract

Keywords

ASJC Scopus subject areas

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