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Displaying 2041 – 2060 of 2377

Symmetry of minimizers with a level surface parallel to the boundary

Giulio Ciraolo, Rolando Magnanini, Shigeru Sakaguchi (2015)

Journal of the European Mathematical Society

We consider the functional $ℐ_{Ω} (v) = \int_{Ω} [f (| D v |) - v] d x,$ where $Ω$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$ , Crasta [Cr1] has shown that if $ℐ_{Ω}$ admits a minimizer in $W_{0}^{1, 1} (Ω)$ depending only on the distance from the boundary of $Ω$ , then $Ω$ must be a ball. With some restrictions on $f$ , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...

Symplectic Pontryagin approximations for optimal design

Jesper Carlsson, Mattias Sandberg, Anders Szepessy (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The powerful Hamilton-Jacobi theory is used for constructing regularizations and error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method for optimal design and reconstruction: the first, analytical, step is to regularize the hamiltonian; next the solution to its stationary hamiltonian system, a nonlinear partial differential equation, is computed with the Newton method. The method is efficient for designs where the hamiltonian function can be...

Symplectic Pontryagin approximations for optimal design

Jesper Carlsson, Mattias Sandberg, Anders Szepessy (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The powerful Hamilton-Jacobi theory is used for constructing regularizations and error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method for optimal design and reconstruction: the first, analytical, step is to regularize the Hamiltonian; next the solution to its stationary Hamiltonian system, a nonlinear partial differential equation, is computed with the Newton method. The method is efficient for designs where the Hamiltonian function...

Syntheses of differential games and pseudo-Riccati equations.

You, Yuncheng (2002)

Abstract and Applied Analysis

Synthesis of stochastic optimal control for a convex optimization problem in Hilbert spaces

Gianluca Gorni (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studia il problema della sintesi per un problema di controllo stocastico con equazione di stato lineare e funzione costo convessa.

System of general variational inequalities involving different nonlinear operators related to fixed point problems and its applications.

Inchan, Issara, Petrot, Narin (2011)

Fixed Point Theory and Applications [electronic only]

System of generalized implicit vector quasivariational inequalities.

Peng, Jian-Wen, Zheng, Xiao-Ping (2007)

Journal of Inequalities and Applications [electronic only]

Systems of generalized quasivariational inclusion problems with applications in $L Γ$ -spaces.

Yang, Ming-Ge, Xu, Jiu-Ping, Huang, Nan-Jing (2011)

Fixed Point Theory and Applications [electronic only]

Systems of singular BVPs - existence of solutions and their properties

Aleksandra Orpel (2014)

Banach Center Publications

We discuss the existence and properties of solutions for systems of singular second-order ODEs in both sublinear and superlinear cases. Our approach is based on the variational method enriched by some topological ideas. We also investigate the continuous dependence of solutions on functional parameters.

The blocking of an inhomogeneous Bingham fluid. Applications to landslides

Patrick Hild, Ioan R. Ionescu, Thomas Lachand-Robert, Ioan Roşca (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This work is concerned with the flow of a viscous plastic fluid. We choose a model of Bingham type taking into account inhomogeneous yield limit of the fluid, which is well-adapted in the description of landslides. After setting the general threedimensional problem, the blocking property is introduced. We then focus on necessary and sufficient conditions such that blocking of the fluid occurs. The anti-plane flow in twodimensional and onedimensional cases is considered. A variational formulation...

The blocking of an inhomogeneous Bingham fluid. Applications to landslides

Patrick Hild, Ioan R. Ionescu, Thomas Lachand-Robert, Ioan Roşca (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The cancellation law for inf-convolution of convex functions

Dariusz Zagrodny (1994)

Studia Mathematica

Conditions under which the inf-convolution of f and g $f □ g (x) : = i n f_{y + z = x} (f (y) + g (z))$ has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions $f : X \to ℝ \cup + \infty$ on a reflexive Banach space such that $l i m_{∥ x ∥ \to \infty} f (x) / ∥ x ∥ = \infty$ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.

The catenary (almost) everywhere.

Gil, Juan B. (2005)

Boletín de la Asociación Matemática Venezolana

The concentration-compactness principle in the calculus of variations. The locally compact case, part 1

P. L. Lions (1984)

Annales de l'I.H.P. Analyse non linéaire

The concentration-compactness principle in the calculus of variations. The locally compact case, part 2

P. L. Lions (1984)

Annales de l'I.H.P. Analyse non linéaire

The concentration-compactness principle in the calculus of variations. The limit case, Part II.

Pierre-Louis Lions (1985)

Revista Matemática Iberoamericana

This paper is the second part of a work devoted to the study of variational problems (with constraints) in functional spaces defined on domains presenting some (local) form of invariance by a non-compact group of transformations like the dilations in RN. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sobolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle and method...

The concentration-compactness principle in the calculus of variations. The limit case, Part I.

Pierre-Louis Lions (1985)

Revista Matemática Iberoamericana

After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in RN where the invariance of RN by the group of dilatations creates some possible loss of compactness. This is for example the case for all the problems associated with the determination of extremal functions in functional inequalities (like for example the Sobolev inequalities). We show here how the concentration-compactness...

The constructive approach on existence of time optimal controls of system governed by nonlinear equations on Banach spaces.

Wang, Jinrong, Xiang, X., Wei, W. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

The convex analysis of unitarily invariant matrix functions.

Lewis, A.S. (1995)

Journal of Convex Analysis

The Dirichlet Energy of Mappings with values into the sphere.

Mariano Giaquinta, Giuseppe Modica (1989)

Manuscripta mathematica

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