Abstract
We consider the following class of second order differential operators d d
where a(x) is a positive semi-definite symmetric matrix which has quadratic growth and b(x) is a vector field of class C 2 which has linear growth. We assume that the mapping a : ℝd → ℒ(ℝd) is also of class C 2 with bounded second derivatives, so that it can be written as a(x) = ½σxσ* x, x∈ℝd, for some matrix valued function σ : ℝd → ℒ(ℝd) which is Lipschitz-continuous (for a proof of this fact see [66] and also [114]. Here we assume further regularity for o; namely we assume that a can be factorized by some a which is twice differentiable with bounded derivatives.
Keywords
- Degenerate Case
- Analytic Semigroup
- Stochastic Partial Differential Equation
- Quadratic Growth
- Order Differential Operator
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). Analyticity of the semigroup in a degenerate case. 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_4
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DOI: https://doi.org/10.1007/3-540-45147-1_4
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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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