# A complex parabolic type monge-ampère equation

A complex parabolic type monge-ampère equation 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 $$C(\bar B \times (0,T)) \cap W_{\infty ,loc}^{2,1} (B \times (0,T))$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A complex parabolic type monge-ampère equation

, Volume 35 (3) – May 1, 1997
18 pages

/lp/springer_journal/a-complex-parabolic-type-monge-amp-re-equation-u36TF8r29Z
Publisher
Springer-Verlag
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
D.O.I.
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 OptimizationSpringer Journals

Published: May 1, 1997

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