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 ℂd,d>1, and Γ is the parabolic boundary ofB × (0,T). Solutionu is proved unique in the class\(C(\bar B \times [0,T]) \cap W_{\infty ,loc}^{2,1} (B \times (0,T))\).
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Spiliotis, J. A complex parabolic type monge-ampère equation. Appl Math Optim 35, 265–282 (1997). https://doi.org/10.1007/BF02683331
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DOI: https://doi.org/10.1007/BF02683331