Differential and Integral Equations

Generation of analytic semigroups and domain characterization for degenerate elliptic operators with unbounded coefficients arising in financial mathematics. I

Fausto Gozzi, Roberto Monte, and Vincenzo Vespri

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Abstract

In this paper we study the generation of analytic semigroup in the space $L^2(\mathbb R^d)$, and the characterization of the domain, for a family of degenerate elliptic operators with unbounded coefficients, which includes some well-known operators arising in Mathematical Finance. To prove the generation of analytic semigroups, the operators of the family are assumed to satisfy suitable growth and compensation conditions. Under stronger assumptions, we obtain also the characterization of the domain. Finally, various consequences of the obtained results are considered in connection with some applications (see, e.g., [6] for financial applications). In a forthcoming paper, part II of this work, we shall examine the problem of the generation of analytic semigroup in $L^p((\mathbb R^d)$, where $p\in(2,+\infty]$, and the characterization of the domain, for the same family of operators.

Article information

Source
Differential Integral Equations, Volume 15, Number 9 (2002), 1085-1128.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060765

Mathematical Reviews number (MathSciNet)
MR1919764

Zentralblatt MATH identifier
1033.47028

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 35J70: Degenerate elliptic equations 35K65: Degenerate parabolic equations 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 91B28

Citation

Gozzi, Fausto; Monte, Roberto; Vespri, Vincenzo. Generation of analytic semigroups and domain characterization for degenerate elliptic operators with unbounded coefficients arising in financial mathematics. I. Differential Integral Equations 15 (2002), no. 9, 1085--1128. https://projecteuclid.org/euclid.die/1356060765


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