Displaying similar documents to “Error estimates for scalar conservation laws by a kinetic approach.”

Towards a two-scale calculus

Augusto Visintin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We define and characterize weak and strong in , and other spaces a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive two-scale...

Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

Silvia Cingolani, Louis Jeanjean, Simone Secchi (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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In this work we consider the magnetic NLS equation ( i - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in N ( 0 . 1 ) where N 3 , A : N N is a magnetic potential, possibly unbounded, V : N is a multi-well electric potential, which can vanish somewhere, f is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution u : N to (0.1), under conditions on the nonlinearity which are nearly optimal.