Uniqueness of solutions of the Cauchy problem of a parabolic equation, and the related question of analyticity with respect to time, depend on global properties of the solution. We demonstrate that if the growth of the initial function (and, if relevant, of the inhomogeneous part and its derivatives) is not too great, solutions of non-stationary parabolic equations whose coefficients belong to quasi-analytic classes are quasi-analytic with respect to all variables and hence are unique. This study is motivated by the problem of endogenous completeness in continuous-time financial markets

Kannai, Y., & Raimondo, R. (2013). Quasi-analytic solutions of linear parabolic equations. JOURNAL D'ANALYSE MATHEMATIQUE, 119(1), 115-145 [10.1007/s11854-013-0004-3].

Quasi-analytic solutions of linear parabolic equations.

RAIMONDO, ROBERTO
2013

Abstract

Uniqueness of solutions of the Cauchy problem of a parabolic equation, and the related question of analyticity with respect to time, depend on global properties of the solution. We demonstrate that if the growth of the initial function (and, if relevant, of the inhomogeneous part and its derivatives) is not too great, solutions of non-stationary parabolic equations whose coefficients belong to quasi-analytic classes are quasi-analytic with respect to all variables and hence are unique. This study is motivated by the problem of endogenous completeness in continuous-time financial markets
Articolo in rivista - Articolo scientifico
Parabolic equations, quasi-analytic functions
English
115
145
31
Kannai, Y., & Raimondo, R. (2013). Quasi-analytic solutions of linear parabolic equations. JOURNAL D'ANALYSE MATHEMATIQUE, 119(1), 115-145 [10.1007/s11854-013-0004-3].
Kannai, Y; Raimondo, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/102393
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