Abstract
With the same notations used in the previous chapter, we can introduce the following second order infinite dimensional differential operator
\( \mathcal{L}(x,D) \) 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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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Kolmogorov equations in Hilbert spaces. In: Cerrai, S. (eds) Second Order PDE’s in Finite and Infinite Dimension. Lecture Notes in Mathematics, vol 1762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45147-1_6
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DOI: https://doi.org/10.1007/3-540-45147-1_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42136-8
Online ISBN: 978-3-540-45147-1
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