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Nonnegative solutions of parabolic operators with low-order terms. (English) Zbl 1040.31006
The author considers the parabolic operator \[ L={\partial \over \partial t}-\text{div}(A(x,t) \nabla_{x})+B(x,t)\cdot \nabla_{x} \] defined on \(\Omega=D\times ]0,T[\), where \(D\) is a bounded \(C^{1,1}\)-domain in \(\mathbb{R}^{n}\) (\(0<T<\infty\)). The matrix \(A\) is assumed to be bounded, real, symmetric and uniformly elliptic. The vector \(B\) is assumed to be in a parabolic Kato class. The main results in this paper are the integral representation theorem and the existence of nontangential limits on the boundary of \(\Omega\) for nonnegative solutions.

MSC:
31B25 Boundary behavior of harmonic functions in higher dimensions
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35C15 Integral representations of solutions to PDEs
31C35 Martin boundary theory
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
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