Kolmogorov equations in Hilbert spaces

Part of the Lecture Notes in Mathematics book series (LNM, volume 1762)


With the same notations used in the previous chapter, we can introduce the following second order infinite dimensional differential operator
$$ \mathcal{L}(x, D) = \frac{1} {2}{\text{Tr[}}D^2 QQ^* ] + \left\langle {Ax + F(x),D} \right\rangle _H , x \in D (A). $$
\( \mathcal{L}(x,D) \) is the diffusion operator corresponding to the system (4.0.1). In this chapter we want to study existence, uniqueness and optimal regularity in Holder spaces for the solutions of the parabolic and the elliptic problems associated with the operator \( \mathcal{L}(x,D) \) .


HILBERT Space Elliptic Problem Strong Solution Parabolic Problem KOLMOGOROV Equation 
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© Springer-Verlag Berlin Heidelberg 2001

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