Uniqueness of solutions to weak parabolic equations for measures | Zendy

Bogachev V. I. | Zendy; Da Prato G. | Zendy; Röckner M. | Zendy; Stannat W. | Zendy

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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

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.

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