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Showing 1 to 6 of 6 for “"Monge Ampere"”.
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ΜΙΑ ΠΙΘΑΝΟΘΕΩΡΗΤΙΚΗ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΕΞΙΣΩΣΗΣ MONGE-AMPERE
… OF THE GENERALISED SOLUTION OF THE REAL MONGE-AMPERE EQUATION MU=F>0 K D, K=Φ ON ΘD, D C IRD OPEN-BOUNDED CONVEX. PARTLY IN PARALLEL TO THE WORK BY B. GAVEAN, WHO TREATED THE COMPLEX CASE, GENERAL RESULTS ARE OBTAINED. SPECIFICALLY THE SOLUTION CAN BE STOCHASTICALLY REPRESENTED IF O<F E L …
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Degenerate Monge-Ampere equations over projective manifolds
In this thesis, we study degenerate Monge-Ampere equations over projective manifolds. The main degeneration is on the cohomology class which is Kähler in classic cases. Our main results concern the case when this class is semi-ample and big with certain generalization to more general cases. Two …
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Local Regularity of the Complex Monge-Ampere Equation
… in the local regularity theory of the complex Monge-Ampere equation through the modern fully-nonlinear PDE point of view. We have apply the modern elliptic techniques to establish new local regularity results. These includes: regularity of small perturbed solutions, Holder regularity of the …
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Higher canonical asymptotics of Kähler-Einstein metrics on quasi-projective manifolds
… We first develop the analysis of the Monge-Ampere operators on these weighted spaces. We construct a family of linear elliptic operators which can be viewed as certain conjugacies of the specially linearized Monge-Ampbre operators. We derive a theorem of Fredholm alternative for such …
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Nonlinear PDE and Optical Surfaces Design
… square law of irradiance. The problem leads to a Monge-Ampere type inequality. The surfaces in the first model are strictly convex and require to be far from the source to avoid obstruction. In the second model, the reflectors are neither convex nor concave and do not block the rays even if they …
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On Generalized Solutions to Some Problems in Electromagnetism and Geometric Optics
… (defined similarly to Brenier solutions for the Monge-Amp\`ere equation) to these problems, both in the near and the far field. The far field problem can be treated using Optimal Transport techniques; as such, a fully nonlinear PDE of Monge-Amp\`ere type arises here.