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Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
5
votes
2
answers
793
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Bedford-Taylor theory
The Dirichlet problem for the Complex Monge-Ampere equation on a bounded pseudoconvex domain in $\mathbb{C}^n$ was studied in Bedford-Taylor's seminal paper wherein they defined $(dd^{c} u)^n$ for loc …
1
vote
Solutions of the $\overline{\partial}$ equation in the upper half-plane
You may transform the problem into one on the unit disc. Then the theory in "The Neumann problem for the Cauchy Riemann complex" might apply. You may also try to solve the equation by hand on the unit …