On the L^p -Theory of Anisotropic Singular Perturbations of Elliptic Problems

Ogabi Chokri (1)

1 Académie de Grenoble

In this article we give an extension of the L 2 theory of anisotropic singular perturbations for elliptic problems. We study a linear and some non-linear problems involving L p data (1 < p < 2). Convergences in pseudo Sobolev spaces are proved for weak and entropy solutions, and rate of conver-gence is given in cylindrical domains

Dans cet article on donne une extension de la théorie L^2 des problèmes de perturbations singulières elliptiques. On étudie certains problèmes linéaires et non-linéaires dans Lp ( 1

Mots clés: L^{p}-theory; entropy solutions; Asymptotic behaviour; Anisotropic singular perturbations; elliptic problem; rate of convergence

Mots clés: Perturbations singulières; Taux de convergence; Théorie Lp; Problèmes elliptiques; Solution entropique; Comportement asymptotique

Domaines: Equations aux dérivées partielles [math.AP]

Ogabi Chokri. On the L^p -Theory of Anisotropic Singular Perturbations of Elliptic Problems. Communications on Pure and Applied Analysis, 2016. ⟨hal-01111759v2⟩