Some remarks on essential self‐adjointness and ultracontractivity of a class of singular elliptic operators
Michael M. H. Pang · Mathematische Nachrichten · 2008
Abstract We study the properties of essential self‐adjointness on C∞c (ℝN ) and semigroup ultracontractivity of a class of singular second order elliptic operators equation image defined in L2 (ℝN , σ–a –N (x) dx) with Dirichlet boundary conditions, where a, b ∈ ℝ and σ: ℝN → (0, ∞) is a C∞‐function satisfying c‐1(1 + |x |) ≤ σ (x) ≤ c (1 + |x |) (x ∈ ℝN). 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)