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Palabras claves o descriptores: FUNDAMENTAL SOLUTIONS (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Felmer , patricio L. ; Quaas, Alexander
Título: Fundamental solutions and two properties of elliptic maximal and minimal operators
Páginas/Colación: pp. 5721-5736
Fecha: November 2009
Transactions of the American Mathematical Society Vol. 361, no.11 November 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: EXTREMAL OPERATORS EXTREMAL OPERATORS, Palabras: FUNDAMENTAL SOLUTIONS FUNDAMENTAL SOLUTIONS, Palabras: LIOUVILLE-TYPE THEOREMS LIOUVILLE-TYPE THEOREMS, Palabras: REMOVABILITY OF SINGULARITIES REMOVABILITY OF SINGULARITIES, Palabras: VISCOSITY SOLUTIONS VISCOSITY SOLUTIONS

Resumen
We study the transverse Lusternik-Schnirelmann category theory of a Riemannian foliation on a closed manifold

For a large class of nonlinear second order elliptic differential operators, we define a concept of dimension, upon which we construct a fundamental solution. This allows us to prove two properties associated to these operators, which are generalizations of properties for the Laplacian and Pucci's operators. If $ {\mathcal M}$denotes such an operator, the first property deals with the possibility of removing singularities of solutions to the equation

$\displaystyle {\mathcal M}(D^2 u)-u^p=0,$   in$\displaystyle \quad B\setminus \{0\}, $

where $ B$is a ball in $ \mathbb{R}^N$. The second property has to do with existence or nonexistence of solutions in $ R^N$to the inequality

$\displaystyle {\mathcal M}(D^2 u)+u^p\le 0,$   in$\displaystyle \quad \mathbb{R}^N. $

In both cases a common critical exponent defined upon the dimension number is obtained, which plays the role of $ N/(N-2)$for the Laplacian.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Liu, Kai
Título: The Fundamental Solution and Its Role in the Optimal Control of Infinite Dimensional Neutral Systems
Páginas/Colación: 1-38 pp.
Fecha: 2009
Applied Mathematics & Optimization: An International Journal with Applcations to Stochastics Vol. 60, no. 1 August 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: FUNDAMENTAL SOLUTIONS FUNDAMENTAL SOLUTIONS, Palabras: OPTIMAL CONTROL OPTIMAL CONTROL

Resumen
In this work, we shall consider standard optimal control problems for a class of neutral functional differential equations in Banach spaces. As the basis of a systematic theory of neutral models, the fundamental solution is constructed and a variation of constants formula of mild solutions is established.We introduce a class of neutral resolvents and show that the Laplace transform of the fundamental solution is its neutral resolvent operator. Necessary conditions in terms of the solutions of neutral adjoint systems are established to deal with the fixed time integral convex cost problem of optimality. Based on optimality conditions, the maximum principle for time varying control domain is presented. Finally, the time optimal control problem to a target set is investigated.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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