Existence of solutions to the Hamilton-Jacobi-Bellman equation under quadratic growth conditions

Authors
Ito, K
Citation
K. Ito, Existence of solutions to the Hamilton-Jacobi-Bellman equation under quadratic growth conditions, J DIFF EQUA, 176(1), 2001, pp. 1-28
Citations number
14
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN journal
00220396 → ACNP
Volume
176
Issue
1
Year of publication
2001
Pages
1 - 28
Database
ISI
SICI code
0022-0396(20011010)176:1<1:EOSTTH>2.0.ZU;2-W
Abstract
In this paper we show the existence of solutions with quadratic growth to H amilton-Jacobi Bellman equations. We assume that the Hamiltonian has the qu adratic growth both in x and p. We obtain the explicit Lipschitz bound of s olutions in the weighted sup-norm. Also, we discuss the vanishing viscosity limit of solutions and show the existence of viscosity solutions to the re sulting Hamilton Jacobi equation. (C) 2001 Academic Press.