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.
| Original language | English |
|---|---|
| Pages (from-to) | 115-145 |
| Number of pages | 31 |
| Journal | Journal d'Analyse Mathematique |
| Volume | 119 |
| Issue number | 1 |
| DOIs | |
| State | Published - Apr 2013 |
| Externally published | Yes |
Bibliographical note
Funding Information:∗Parts of the research reported on in this paper were performed while Y. K. was visiting the University of Melbourne. †Raimondo’s work was supported by grant DP0558187 from the Australian Research Council.