Skip to main content

Part of the book series: Birkhäuser Advanced Texts / Basler Lehrbücher ((BAT))

Abstract

In this chapter we would like to consider in more details the Dirichlet problem for the p-Laplace operator, namely, if Ωis an open subset of ℝn, 1 < p < +∞ the problem

$$ \left\{ \begin{gathered} - \partial _{x_i } \left( {\left| {\nabla u} \right|^{p - 2} \partial _{x_i } u} \right) = f in \Omega , \hfill \\ u = 0 on \partial \Omega . \hfill \\ \end{gathered} \right. $$
((1))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Birkhäuser Verlag AG

About this chapter

Cite this chapter

(2009). The p-Laplace Equation. In: Elliptic Equations: An Introductory Course. Birkhäuser Advanced Texts / Basler Lehrbücher. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9982-5_17

Download citation

Publish with us

Policies and ethics