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Artinian automorphisms of infinite groups

Antonella Leone — 2006

Bollettino dell'Unione Matematica Italiana

An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain H 1 > H 2 > ⋯ > H n > ⋯ of subgroups of G there exists a positive integer m such that ( H n ) a = H n for every n ≥ m . In this paper we show that in many cases the group of all artinian automorphisms of G coincides with the group of all power automorphisms of G .

3D-2D asymptotic analysis for micromagnetic thin films

Roberto Alicandro;  Chiara Leone — 2001

ESAIM: Control, Optimisation and Calculus of Variations

Γ -convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness ε approaches zero of a ferromagnetic thin structure Ω ε = ω × ( - ε , ε ) , ω ⊂ ℝ 2 , whose energy is given by ℰ ε ( m ¯ ) = 1 ε ∫ Ω ε W ( m ¯ , ∇ m ¯ ) + 1 2 ∇ u ¯ · m ¯ d x subject to div ( - ∇ u ¯ + m ¯ χ Ω ε ) = 0 on ℝ 3 , and to the constraint | m ¯ | = 1 on Ω ε , where W is any continuous function satisfying p -growth assumptions with p > 1 . Partial results are also obtained in the case p = 1 , under an additional assumption...

3D-2D Asymptotic Analysis for Micromagnetic Thin Films

Roberto Alicandro;  Chiara Leone — 2010

ESAIM: Control, Optimisation and Calculus of Variations

-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness approaches zero of a ferromagnetic thin structure Ω ε = ω × ( - ε , ε ) , ω ⊂ ℝ 2 , whose energy is given by ℰ ε ( m ¯ ) = 1 ε ∫ Ω ε W ( m ¯ , ∇ m ¯ ) + 1 2 ∇ u ¯ · m ¯ d x subject to div ( - ∇ u ¯ + m ¯ χ Ω ε ) = 0 on ℝ 3 , and to the constraint | m ¯ | = 1 on Ω ε , where is any continuous function satisfying -growth assumptions with . Partial results are also obtained in the case , under an additional assumption on .

Obstacle problems for scalar conservation laws

Laurent Levi — 2001

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

In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in L ∞ . Lastly, we study the behaviour of this solution and its stability properties with...

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