Results 21 to 27 of about 190 (27)
On the second boundary value problem for Monge-Ampere type equations and geometric optics
, 2018 In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability of optimal ...
Jiang, Feida, Trudinger, Neil S.
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Prohibiting isolated singularities in optimal transport [PDF]
, 2014 We give natural topological conditions on the support of the target measure under which solutions to the optimal transport problem with cost function satisfying the (weak) Ma, Trudinger, and Wang condition cannot have any isolated singular points.Comment:
Kim, Young-Heon, Kitagawa, Jun
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Stability and regularity of solutions of the Monge-Amp\`ere equation on Hermitian manifolds
, 2019 We prove stability of solutions of the complex Monge-Amp\`ere equation on compact Hermitian manifolds, when the right hand side varies in a bounded set in $L^p, p>1$ and it is bounded away from zero. Such solutions are shown to be H\"older continuous. As
Kolodziej, Slawomir, Nguyen, Ngoc Cuong
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Advances in Nonlinear AnalysisIn this article, our main aim is to investigate the existence of radial kk-convex solutions for the following Dirichlet system with kk-Hessian operators: Sk(D2u)=λ1ν1(∣x∣)(−u)p1(−v)q1inℬ(R),Sk(D2v)=λ2ν2(∣x∣)(−u)p2(−v)q2inℬ(R),u=v=0on∂ℬ(R).\left\{\begin ...
He Xingyue, Gao Chenghua, Wang Jingjing
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Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Amp\`ere Equations
, 2015 We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target.
Brix, Kolja +2 more
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Problems for P-Monge-Ampere Equations [PDF]
, 2012 2010 Mathematics Subject Classification: 35A23, 35B51, 35J96, 35P30, 47J20, 52A40.We consider the homogeneous Dirichlet problem for a class of equations which generalize the p-Laplace equations as well as the Monge- Amp`ere equations in a strictly convex
Anedda, Claudia +2 more
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, 2018 We obtain the H\"older regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity.
Le, Nam Q.
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