Results 21 to 30 of about 210 (47)

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
core  

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, Hafizogullari, Yasemin, Platen, Andreas   +2 more
core   +1 more source

Removable Singularities of $m$-Hessian Equations

, 2016
In this paper we give a new, less restrictive condition for removability of singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in $\Omega \setminus E$, $\Omega \subset \mathbb ...
Car, Hülya, Pröpper, René
core   +1 more source

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.
core   +1 more source

H\"older regularity of the 2D dual semigeostrophic equations via analysis of linearized Monge-Amp\`ere equations

, 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.
core   +1 more source

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, Cadeddu, Lucio, Porru, Giovanni   +2 more
core  

k-convex solutions for multiparameter Dirichlet systems with k-Hessian operator and Lane-Emden type nonlinearities

Advances in Nonlinear Analysis
In 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
doaj   +1 more source

The existence and asymptotic behavior of large solutions to the k-Hessian equations with nonlinear gradient terms

Advances in Nonlinear Analysis
In this paper, we establish the first- and second-order asymptotic behaviors (expansions) of boundary blow-up solutions to the k-Hessian problem Sk(D2u)=b(x)f(u)C0+∇u2q/2 in Ω,u=+∞ on ∂Ω. ${S}_{k}\left({D}^{2}u\right)=b\left(x\right)f\left(u\right){\left(
Wan Haitao
doaj   +1 more source

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A class of prescribed Weingarten curvature equations in Euclidean space

Communications in Partial Differential Equations, 2021
Qiang Tu
exaly  

The Minkowski problem in Gaussian probability space

Advances in Mathematics, 2021
Yong Huang, Dongmeng Xi, Yiming Zhao
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