Heat kernel estimates for the Dirichlet fractional Laplacian

• Autores: Zhen-Qing Chen, Panki Kim, Renming Song
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 12, Nº 5, 2010, págs. 1307-1329
• Idioma: inglés
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• Resumen

  • In this paper, we consider the fractional Laplacian -(-?)a/2 on an open subset in Rd with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C1.1 open sets. This heat kernel is also the transition density of a rotationally symmetric a-stable process killed upon leaving a C1.1 open set. Our results are the first sharp two-sided estimates for the Dirichlet heat kernel of a non-local operator on open sets.