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Applied Mathematics and Optimization

, Volume 35, Issue 3, pp 265–282 | Cite as

A complex parabolic type monge-ampère equation

  • J. Spiliotis
Article
  • 66 Downloads

Abstract

The complex parabolic type Monge-Ampère equation we are dealing with is of the form\((\partial u/\partial t){\text{ det[}}\partial ^2 u/\partial z_i {\text{ }}\partial \overline z _j ] = f\) inB × (0,T),u=ϕ on Γ, whereB is the unit ball in ℂ d ,d>1, and Γ is the parabolic boundary ofB × (0,T). Solutionu is proved unique in the class\(C(\bar B \times [0,T]) \cap W_{\infty ,loc}^{2,1} (B \times (0,T))\).

Key Words

Monge-Ampère Complex First-initial Boundary Parabolic Stochastic integral Control 

AMS Classification

93E20 35K60 60H30 

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Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • J. Spiliotis
    • 1
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece

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