Topic outline

  • General

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  • The p-Laplace equation

    The most important partial differential equation of the second order is the celebrated

    Laplace equation. This is the prototype for linear elliptic equations. It is

    less well-known that it also has a non-linear counterpart, the so-called p-Laplace

    equation (or p-harmonic equation), depending on a parameter p. The p-Laplace

    equation has been much studied during the last fifty years and its theory is by now

    rather developed. Some challenging open problems remain. The p-Laplace equation

    is a degenerate or singular elliptic equation in divergence form. It deserves a

    treatise of its own, without any extra complications and generalizations. This is

    my humble attempt to write such a treatise. Perhaps the interested reader wants to

    consult the monograph Nonlinear Potential Theory of Degenerate Elliptic Equations

    by J. Heinonen, T. Kilpel¨ainen and O. Martio, when it comes to more advanced and

    general questions.

  • Fiche de contact

    • Enseignant de la matière : Dr. Kamila Kachekouche,   Contact : kamila.kachekouche01@gmail.com
    • Faculté de sciences
    • Département de Mathematiques
    • Filière : Mathematiques
    • Niveau : M1 commun
    • Unité d'enseignement : Fondamentale
    • Coefficient : 2
    • Crédit : 4
    • Volume horaire de travail requis/semaine : 1h
    • Modalité du suivi : Dimanche de 10h00 à 11h00.
    • Modalité d'évaluation : TP 50%, Examen finale 50%.
    • Note du CC = 20% Moyenne des tests + 20% Devoir 1 + 20% Devoir 2 + 20% Devoir 3 + 20 % Présence et participation.

  • Objectifs de la matière

    ce cours donne les propriétés de l'operateur p-Laplace  qui vous aide dans l'étude mathématique d'une equations  avec l'operateur p-Laplacien

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