On the optimal control method in quaternionic analysis

DOI10.1016/j.bulsci.2011.09.004zbMath1238.49007OpenAlexW2020092667MaRDI QIDQ653657

Wei Wang

Publication date: 19 December 2011

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2011.09.004

zbMATH Keywords

optimal control methodquaternionic control and stochastic integralsquaternionic Monge--Ampère operatorquaternionic plurisubharmonic functionsquaternionic regular functions

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Nonlinear elliptic equations (35J60) Existence theories for optimal control problems involving partial differential equations (49J20) Plurisubharmonic functions and generalizations (32U05)

Related Items (17)

Viscosity solutions to quaternionic Monge-Ampère equations ⋮ On the linear algebra in the quaternionic pluripotential theory ⋮ On the Hodge-type decomposition and cohomology groups of \(k\)-Cauchy-Fueter complexes over domains in the quaternionic space ⋮ On the Cauchy-Szegő kernel for quaternion Siegel upper half-space ⋮ On Radon-Penrose transformation and \(k\)-Cauchy-Fueter operator ⋮ The Neumann problem for the \(k\)-Cauchy-Fueter complex over \(k\)-pseudoconvex domains in \(\mathbb{R}^4\) and the \(L^2\) estimate ⋮ A variational approach to the quaternionic Monge-Ampère equation ⋮ Quasicontinuity and maximality of quaternionic plurisubharmonic functions ⋮ Quaternionic Monge-Ampère operator for unbounded plurisubharmonic functions ⋮ Sub-Riemannian Geometry and Hypoelliptic Operators ⋮ The continuity and range of the quaternionic Monge-Ampère operator on quaternionic space ⋮ The quaternionic Monge-Ampère operator and plurisubharmonic functions on the Heisenberg group ⋮ The tangential \(k\)-Cauchy-Fueter complexes and Hartogs' phenomenon over the right quaternionic Heisenberg group ⋮ Hölder continuous solutions to quaternionic Monge-Ampère equations ⋮ On the tangential Cauchy-Fueter operators on nondegenerate quadratic hypersurfaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {H}^2}$\end{document} ⋮ The Cauchy-Szegö kernel for the Hardy space of 0-regular functions on the quaternionic Siegel upper half space ⋮ On the quaternionic Monge-Ampère operator, closed positive currents and Lelong-Jensen type formula on the quaternionic space

Cites Work

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• The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group
• On non-homogeneous Cauchy-Fueter equations and Hartogs' phenomenon in several quaternionic variables
• The Dirichlet problem for a complex Monge-Ampère equation
• Méthodes de contrôle optimal en analyse complexe. I: Résolution d'équation de Monge Ampère
• Méthode de contrôle optimal en analyse complexe ou réelle. III. Diffusion des fonctions plurisousharmoniques ou convexes
• Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
• Quaternionic Monge-Ampère equations
• Analysis of Dirac systems and computational algebra.
• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables.
• The \(k\)-Cauchy-Fueter complex, Penrose transformation and hartogs phenomenon for quaternionic \(k\)-regular functions
• Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry
• On a Generalized Dirichlet Problem for Plurisubharmonic Functions and Pseudo-Convex Domains. Characterization of Silov Boundaries

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