The p-Laplace Equations and Systems

Wang, Mingxin; Pang, Peter Y. H.

doi:10.1007/978-981-99-8692-7_7

Mingxin Wang³ &
Peter Y. H. Pang⁴

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Abstract

In this chapter we mainly focus on the properties of the operator

$$\displaystyle \begin{array}{@{}rcl@{}} \mathscr {L}_p^au:=-\varDelta _pu+a(x)|u|{ }^{p-2}u \end{array} $$

and the corresponding boundary value problems of equations and systems in $\varOmega $, where

$$\displaystyle \varDelta _p u=\mathrm {div}\big (|\nabla u|{ }^{p-2}\nabla u\big ) $$

is the p-Laplacian of u, $\varOmega $ is a bounded and smooth domain in $\mathbb {R}^n$, $1<p<\infty $, and $a\in L^\infty (\varOmega )$. Throughout this chapter, we shall denote

$$\displaystyle p'=p/(p-1)\;\;\;\text{ for}\;\; 1<p<\infty . $$

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School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan, China
Mingxin Wang
National University of Singapore, Singapore, Singapore
Peter Y. H. Pang

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Mingxin Wang
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Wang, M., Pang, P.Y.H. (2024). The p-Laplace Equations and Systems. In: Nonlinear Second Order Elliptic Equations. Springer, Singapore. https://doi.org/10.1007/978-981-99-8692-7_7

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DOI: https://doi.org/10.1007/978-981-99-8692-7_7
Published: 09 January 2024
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-8691-0
Online ISBN: 978-981-99-8692-7
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