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Uniqueness of solutions to weak parabolic equations for measures
Author(s) -
Bogachev V. I.,
Da Prato G.,
Röckner M.,
Stannat W.
Publication year - 2007
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/bdm046
Subject(s) - mathematics , uniqueness , lipschitz continuity , measure (data warehouse) , operator (biology) , mathematical analysis , type (biology) , parabolic partial differential equation , pure mathematics , differential equation , ecology , biochemistry , chemistry , repressor , database , biology , computer science , transcription factor , gene
Abstract We study uniqueness of solutions of parabolic equations for measures μ ( dt dx ) = μ t ( dx ) dt of the type L * μ = 0, satisfying μ t → ν as t → 0, where each μ t is a probability measure onR d , L = ∂ t + a i j ( t , x ) ∂ x i∂ x j+ b i ( t , x ) ∂ x jis a differential operator on (0, T ) × ℝ d and ν is a given initial measure. One main result is that uniqueness holds under uniform ellipticity and Lipschitz conditions on a ij but for b i merely local integrability and coercivity conditions are sufficient.