Existence and compactness for weak solutions to Bellman systems with critical growth
| Type of publication: | Article |
| Citation: | |
| Publication status: | Published |
| Journal: | Discrete and Continuous Dynamical Systems - Series B |
| Volume: | 17 |
| Number: | 6 |
| Year: | 2012 |
| Pages: | 1729--1750 |
| Note: | Preprint NCMM No 2011-012 |
| URL: | http://www.karlin.mff.cuni.cz/... |
| DOI: | 10.3934/dcdsb.2012.17.1729 |
| Abstract: | We deal with nonlinear elliptic and parabolic systems that are the Bellman systems associated to stochastic di erential games as a main motivation. We establish the existence of weak solutions in any dimension for an arbitrary number of equations (\players"). The method is based on using a renormalized sub- and super-solution technique. The main novelty consists in the new structure conditions on the critical growth terms with allow us to show weak solvability for Bellman systems to certain classes of stochastic di erential games. |
| Keywords: | Bellman equation, Hamiltonians, nonlinear elliptic equations, renor- malized sub- and super-solutions., Stochastic games, weak lower- and upper- stability, weak solution |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
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