Existence and compactness for weak solutions to bellman systems with critical growth
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We deal with nonlinear elliptic and parabolic systems that are the Bellman systems associated to stochastic differential 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 differential games.
"This research was supported by WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (R31-20007). . . . The support of the Collaborative Research Center (SFB 611) is also acknowledged."