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On Aronson's Upper Bounds for Heat Kernels
Author(s) -
Bass Richard F.
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008918
Subject(s) - mathematics , upper and lower bounds , mathematics subject classification , operator (biology) , divergence (linguistics) , heat equation , heat kernel , combinatorics , pure mathematics , mathematical analysis , chemistry , biochemistry , linguistics , philosophy , repressor , transcription factor , gene
Let L be a uniformly elliptic operator in divergence form on R d , and let p ( t,x,y ) be the fundamental solution to the heat equation for L. A new proof is given of Aronson's upper bound: p ( t , x , y ) ⩽ c 1 t − d / 2 exp ( − c 2| x − y | 2 / t ) .2000 Mathematics Subject Classification 35J15, 60J60.