# 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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations