Nonautonomous Kolmogorov Parabolic Equations with Unbounded Coefficients
نویسنده
چکیده
We study a class of elliptic operators A with unbounded coefficients defined in I × R for some unbounded interval I ⊂ R. We prove that, for any s ∈ I, the Cauchy problem u(s, ·) = f ∈ Cb(R ) for the parabolic equation Dtu = Au admits a unique bounded classical solution u. This allows to associate an evolution family {G(t, s)} with A, in a natural way. We study the main properties of this evolution family and prove gradient estimates for the function G(t, s)f . Under suitable assumptions, we show that there exists an evolution system of measures for {G(t, s)} and we study the first properties of the extension of G(t, s) to the L-spaces with respect to such measures.
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