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Some remarks on essential self‐adjointness and ultracontractivity of a class of singular elliptic operators
Author(s) -
Pang Michael M. H.
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810660
Subject(s) - mathematics , class (philosophy) , pure mathematics , algebra over a field , mathematical analysis , computer science , artificial intelligence
We study the properties of essential self‐adjointness on C ∞ c (ℝ N ) and semigroup ultracontractivity of a class of singular second order elliptic operatorsdefined in L 2 (ℝ N , σ – a – N ( x ) dx ) with Dirichlet boundary conditions, where a , b ∈ ℝ and σ : ℝ N → (0, ∞) is a C ∞ ‐function satisfyingc ‐1 (1 + | x |) ≤ σ ( x ) ≤ c (1 + | x |) ( x ∈ ℝ N ).We also obtain sharp short time upper and lower diagonal bounds on the heat kernel of e – Ht . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)