Smooth Approximations of the Aleksandrov Solution of the Monge-ampère Equation
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چکیده
We prove the existence of piecewise polynomials strictly convex smooth functions which converge uniformly on compact subsets to the Aleksandrov solution of the Monge-Ampère equation. We extend the Aleksandrov theory to right hand side only locally integrable and on convex bounded domains not necessarily strictly convex. The result suggests that for the numerical resolution of the equation, it is enough to assume that the solution is convex and piecewise smooth.
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