All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 7

Displaying 121 – 133 of 133

Showing per page

Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel, G. Orlandi (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions u ε of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of ℝ N , N ≥ 2 , where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy E ε ( u ε ) verifies the bound (natural in the context) E ε ( u ε ) ≤ M 0 | log ε | , where M 0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of u ε , as ε → 0 , is to establish uniform L p bounds for the gradient, for some p > 1 . We review some recent techniques developed in...

Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel, G. Orlandi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions uE of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of ℝ N , N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy E ε ( u ε ) verifies the bound (natural in the context) E ε ( u ε ) ≤ M 0 | log ε | , where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uE, as ε → 0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some...

Γ -convergence and absolute minimizers for supremal functionals

Thierry Champion, Luigi De Pascale, Francesca Prinari (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove that the L p approximants naturally associated to a supremal functional Γ -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local...

Γ-convergence and absolute minimizers for supremal functionals

Thierry Champion, Luigi De Pascale, Francesca Prinari (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove that the Lp approximants naturally associated to a supremal functional Γ-converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local solution)...

Currently displaying 121 – 133 of 133

Previous Page 7