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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Generation of Analytic Semigroups and Domain Characterization for Degenerate Elliptic Operators with Unbounded Coefficients Arising in Financial Mathematics. Part II
verfasst von : Massimiliano Giuli, Fausto Gozzi, Roberto Monte, Vincenzo Vespri
Erschienen in: Functional Analysis and Evolution Equations
Verlag: Birkhäuser Basel
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This paper is devoted to study the generation of analytic semigroup for a family of degenerate elliptic operators (with unbounded coefficients) which includes well-known operators arising in mathematical finance. The generation property is proved by assuming some compensation conditions among the coefficients and applying a suitable modification of the techniques developed in [
16
]. Using the results proved in [
11
] concerning the generation in the space
L
2
(ℝ
d
), we prove the generation results in
L
p
(ℝ
d
) for
p
∈ [1,+
∞
]. These results have several consequences in connection with the financial applications [
3
,
11
].