Abstract
In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property of Ornstein-Uhlenbeck transition evolution operators for stochastic Cauchy problems in Banach spaces with time-dependent coefficients.
Original language | English (US) |
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Pages (from-to) | 55 - 76 |
Number of pages | 21 |
Journal | Journal Of Mathematics Research |
Volume | 6 |
Issue number | 4 |
State | Published - 2014 |