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Displaying 21 – 40 of 118

Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations

François Alouges, Tristan Rivière, Sylvia Serfaty (2010)

ESAIM: Control, Optimisation and Calculus of Variations

 We study a two-dimensional model for micromagnetics, which consists in an energy functional over S2-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....

Neue Erzeugungen der Minmalflächen von G. Thomsen.

Hermann Schaal (1973)

Monatshefte für Mathematik

New a posteriori $L^{\infty} (L^{2})$ and $L^{2} (L^{2})$ -error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems

Zuliang Lu (2016)

Applications of Mathematics

We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in $L^{\infty} (J; L^{2} (Ω))$ -norm and $L^{2} (J; L^{2} (Ω))$ -norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new, are an important...

New classes of analytic and Gevrey semigroups and applications

Angelo Favini, Roberto Triggiani (1993)

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

We consider the operator $- A + i B$ on a complex Hilbert space, where $A$ is positive self-adjoint and $B$ is self-adjoint, and where, moreover, « $B$ is comparable to $A^{α}$ , $α \geq 1$ », in a technical sense. Two applications are given.

New concepts of well-posedness for optimization problems with variational inequality constraints.

Del Prete, Imma, Lignola, M.Beatrice, Morgan, Jacqueline (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

New convergence results for Nash equilibria.

Morgan, Jacqueline, Raucci, Roberto (1999)

Journal of Convex Analysis

New convexity conditions in the calculus of variations and compensated compactness theory

Krzysztof Chełmiński, Agnieszka Kałamajska (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the lower semicontinuous functional of the form $I_{f} (u) = \int_{Ω} f (u) d x$ where $u$ satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar’s $Λ$ -convexity condition for the integrand $f$ extends to the new geometric conditions satisfied on four dimensional symplexes. Similar conditions on three dimensional symplexes were recently obtained by the second author. New conditions apply to quasiconvex...

New convexity conditions in the calculus of variations and compensated compactness theory

Krzysztof Chełmiński, Agnieszka Kałamajska (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the lower semicontinuous functional of the form $I_{f} (u) = \int_{Ω} f (u) d x$ where u satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar's Λ-convexity condition for the integrand f extends to the new geometric conditions satisfied on four dimensional symplexes. Similar conditions on three dimensional symplexes were recently obtained by the second author. New conditions apply...

New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces.

Wang, Shenghua, Zhou, Caili (2011)

Fixed Point Theory and Applications [electronic only]

New linking theorems

Martin Schechter (1998)

Rendiconti del Seminario Matematico della Università di Padova

New operators on jet spaces

L. Mangiarotti, Marco Modugno (1983)

Annales de la Faculté des sciences de Toulouse : Mathématiques

New perturbed iterations for a generalized class of strongly nonlinear operator inclusion problems in Banach spaces.

Lan, Heng-You, Zeng, Huang-Lin, Li, Zuo-An (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

New regularity results and improved error estimates for optimal control problems with state constraints

Eduardo Casas, Mariano Mateos, Boris Vexler (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence...

New results in subspace-stabilization control theory.

Johnson, C.D. (2000)

Mathematical Problems in Engineering

New results on the classical problem of Plateau on the existence of many solutions

Reinhold Böhme (1981/1982)

Séminaire Bourbaki

New sufficient convergence conditions for the secant method

Ioannis K. Argyros (2005)

Czechoslovak Mathematical Journal

We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses “Lipschitz-type” and center-“Lipschitz-type” instead of just “Lipschitz-type” conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated.

New system of general nonconvex variational inequalities.

Noor, Muhammad Aslam, Noor, Khalida Inayat (2010)

Applied Mathematics E-Notes [electronic only]

New versions on Nikaidô's coincidence theorem

Liang-Ju Chu, Ching-Yan Lin (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions,...

Newton and conjugate gradient for harmonic maps from the disc into the sphere

Morgan Pierre (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We compute numerically the minimizers of the Dirichlet energy $E (u) = \frac{1}{2} \int_{B^{2}} {| \nabla u |}^{2} d x$ among maps $u : B^{2} \to S^{2}$ from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous $P_{1}$ finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which is a preconditioned...

Newton's method in the context of gradients.

Karatson, Janos, Neuberger, John W. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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