The semigroup generated by the Dirichlet Laplacian of fractional order

Iwabuchi, Tsukasa

doi:10.2140/apde.2018.11.683

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The semigroup generated by the Dirichlet Laplacian of fractional order

Tsukasa Iwabuchi

Vol. 11 (2018), No. 3, 683–703

DOI: 10.2140/apde.2018.11.683

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 $ℝ^{d}$ .

Keywords

semigroup, Dirichlet Laplacian, Besov spaces

Mathematical Subject Classification 2010

Primary: 35R11

Secondary: 35K08

Milestones

Received: 4 January 2017

Revised: 30 August 2017

Accepted: 16 October 2017

Published: 22 November 2017

Authors

Tsukasa Iwabuchi
Mathematical Institute Tohoku University Sendai Japan

Vol. 11, No. 3, 2018