Results 21 to 30 of about 162 (135)

On Neumann problem for the degenerate Monge–Ampère type equations

Boundary Value Problems, 2021
In this paper, we study the global C 1 , 1 $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value ...
Juhua Shi, Feida Jiang
doaj   +1 more source

Application of isotropic geometry to the solution of the Monge–Ampere equation

Қарағанды университетінің хабаршысы. Математика сериясы
This paper explores the Monge–Ampere equation in the context of isotropic geometry. The study begins with an overview of the fundamental properties of isotropic space, including its scalar product, distance formula, and the nature of surfaces and ...
Sh.Sh. Ismoilov
doaj   +1 more source

A curvature flow to the Lp Minkowski-type problem of q-capacity

Advanced Nonlinear Studies, 2023
This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
doaj   +1 more source

On an {\it a priori} $L^\infty$ estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds

Cubo, 2022
We investigate Monge-Amp\`ere type equations on almost Hermitian manifolds and show an \textit{a priori} $L^\infty$ estimate for a smooth solution of these equations.
Masaya Kawamura
doaj   +1 more source

Simplified Geometric Approach to Freeform Beam Shaper Design

International Journal of Optics, 2020
Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily.
Jacek Wojtanowski, Tadeusz Drozd
doaj   +1 more source

A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds

Journal of Applied Mathematics, 2013
We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function.
Qiang Ru
doaj   +1 more source

Three‐dimensional single‐shell dielectric lens design using complex coordinates and local axis‐displaced confocal quadrics

IET Microwaves, Antennas & Propagation, 2023
This study proposes an analytical formulation in complex coordinates to synthesise three‐dimensional single‐shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non ...
Aline Rocha deAssis, José Ricardo Bergmann, Fernando José daSilva Moreira   +2 more
doaj   +1 more source

Exponential convergence for ultrafast diffusion equations with log‐concave weights

Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.
Abstract We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log‐concave and log‐lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in Iacobelli [Discrete Contin. Dyn. Syst. 39 (2019), 4929–4943].
Max Fathi, Mikaela Iacobelli
wiley   +1 more source

Singularity of non‐pluripolar cohomology classes

Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.
Abstract We establish a relation between Lelong numbers and the full mass property of relative non‐pluripolar products. We use this relation to prove that if the restricted volume of a big class α$\alpha$ along an effective divisor D$D$ has full mass, then the Lelong numbers of the non‐pluripolar class ⟨αn−1⟩$\langle \alpha ^{n-1}\rangle$ at every ...
Duc‐Bao Nguyen, Shuang Su, Duc‐Viet Vu   +2 more
wiley   +1 more source

Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions

Mathematics
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations.
Andrei D. Polyanin, Alexander V. Aksenov
doaj   +1 more source