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Kolmogorov equations in Hilbert spaces

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

Abstract

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 \( \mathcal{L}(x,D) \) .

Keywords

HILBERT Space Elliptic Problem Strong Solution Parabolic Problem KOLMOGOROV Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

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