Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-complex-parabolic-type-monge-amp-re-equation-u36TF8r29Z
References (14)
-
N. Krylov (1990)
Smoothness of the value function for a controlled diffusion process in a domainMathematics of The Ussr-izvestiya, 34
-
P. Linos (1983)
Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and applicationCommunications in Partial Differential Equations, 8
-
J. Spiliotis (1992)
Certain results on a parabolic type Monge-Ampere equationJournal of Mathematical Analysis and Applications, 163
-
N. Krylov (1982)
ON CONTROLLED DIFFUSION PROCESSES WITH UNBOUNDED COEFFICIENTSMathematics of The Ussr-izvestiya, 19
-
N. Krylov (1976)
Sequences of convex functions and estimates of the maximum of the solution of a parabolic equationSiberian Mathematical Journal, 17
-
A. Friedman (1975)
Stochastic Differential Equations and Applications -
P. Lions (1981)
Control of diffusion processes in RNCommunications on Pure and Applied Mathematics, 34
-
D. Stroock, Srinivasa Varadhan (1979)
Multidimensional Diffusion Processes -
P. Lions (1983)
Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniquenessCommunications in Partial Differential Equations, 8
-
Eric Bedford, B. Taylor (1976)
The dirichlet problem for a complex Monge-Ampère equationInventiones mathematicae, 37
-
B. Gaveau (1977)
Méthodes de contrôle optimal en analyse complexe. I. Résolution d'équations de Monge AmpèreJournal of Functional Analysis, 25
-
N. Krylov (1980)
Controlled Diffusion Processes -
N. Krylov (1971)
ON UNIQUENESS OF THE SOLUTION OF BELLMAN'S EQUATIONMathematics of The Ussr-izvestiya, 5
-
N. Krylov (1969)
On Itô’s Stochastic Integral EquationsTheory of Probability and Its Applications, 14
- Publisher
- Springer Journals
- Copyright
- Copyright © 1997 by Springer-Verlag New York Inc.
- Subject
- Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/BF02683331
- Publisher site
- See Article on Publisher Site
Abstract
The complex parabolic type Monge-Ampère equation we are dealing with is of the form $$(\partial u/\partial t){\text{ det(}}\partial ^2 u/\partial z_i {\text{ }}\partial \overline z _j ) = f$$ in B × (0, T ), u = ϕ on Γ, where B is the unit ball in ℂ d , d >1, and Γ is the parabolic boundary of B × (0, T) . Solution u is proved unique in the class $$C(\bar B \times (0,T)) \cap W_{\infty ,loc}^{2,1} (B \times (0,T))$$ .
Journal
Applied Mathematics and Optimization – Springer Journals
Published: May 1, 1997