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  Volume 8, Issue 2, Article 36
Dirichlet Green Functions for Parabolic Operators with Singular Lower-Order Terms

    Authors: Lotfi Riahi,  
    Keywords: Green function, Parabolic operator, Initial-Dirichlet problem, Boundary behavior, Singular potential, Singular drift term, Radon measure, Schrödinger heat kernel, Parabolic Kato class.  
    Date Received: 15/03/06  
    Date Accepted: 10/04/07  
    Subject Codes:

34B27, 35K10.

    Editors: Sever S. Dragomir,  

We prove the existence and uniqueness of a continuous Green function for the parabolic operator $ L={partial/ {partial t}}-mathrm{div} (A(x,t)nabla_x)+nucdotnabla_x + mu$ with the initial Dirichlet boundary condition on a $ C^{1,1}$-cylindrical domain $ Omegasubset mathbb{R} ^ntimes mathbb{R},  ngeq 1$, satisfying lower and upper estimates, where $ nu=(nu_1,dots ,nu_n),  nu_i$ and $ mu$ are in general classes of signed Radon measures covering the well known parabolic Kato classes.

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