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Heat Kernel (heat + kernel)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Some remarks on essential self-adjointness and ultracontractivity of a class of singular elliptic operators

MATHEMATISCHE NACHRICHTEN, Issue 8 2008
Michael M. H. Pang
Abstract We study the properties of essential self-adjointness on C,c (,N) and semigroup ultracontractivity of a class of singular second order elliptic operators defined in L2 (,N, ,,a ,N(x) dx) with Dirichlet boundary conditions, where a, b , , and ,: ,N , (0, ,) is a C, -function satisfying c -1(1 + |x |) , , (x) , c (1 + |x |) (x , ,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) [source]

Obtaining upper bounds of heat kernels from lower bounds

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2008
Alexander Grigor
We show that a near-diagonal lower bound of the heat kernel of a Dirichlet form on a metric measure space with a regular measure implies an on-diagonal upper bound. If in addition the Dirichlet form is local and regular, then we obtain a full off-diagonal upper bound of the heat kernel provided the Dirichlet heat kernel on any ball satisfies a near-diagonal lower estimate. This reveals a new phenomenon in the relationship between the lower and upper bounds of the heat kernel. © 2007 Wiley Periodicals, Inc. [source]