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L 1 Properties of Second order Elliptic Operators
Author(s) -
Davies E. B.
Publication year - 1985
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/blms/17.5.417
Subject(s) - mathematics , elliptic operator , order (exchange) , semigroup , riemannian manifold , differential operator , spectral theory , operator (biology) , pure mathematics , semi elliptic operator , mathematical analysis , hilbert space , biochemistry , chemistry , repressor , transcription factor , gene , finance , economics
We present a connected account of various spectral and regularity properties of the semigroup associated with a fairly general symmetric second order elliptic operator on a Riemannian manifold. Our main goal is to relate the L 2 theory to the less well understood L 1 theory, and hence to the approach via the theory of stochastic differential equations.