The p-Laplace Equations and Systems

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

Chapter Chapter 7 in Nonlinear Second Order Elliptic Equations, 2024, pp 241-285 from Springer

Abstract: Abstract In this chapter we mainly focus on the properties of the operator L p a u : = − Δ p u + a ( x ) | u | p − 2 u $$\displaystyle \begin{array}{@{}rcl@{}} \mathscr {L}_p^au:=-\varDelta _pu+a(x)|u|{ }^{p-2}u \end{array} $$ and the corresponding boundary value problems of equations and systems in Ω $$\varOmega $$ , where Δ p u = div ( | ∇ u | p − 2 ∇ u ) $$\displaystyle \varDelta _p u=\mathrm {div}\big (|\nabla u|{ }^{p-2}\nabla u\big ) $$ is the p-Laplacianp-Laplacian of u, Ω $$\varOmega $$ is a bounded and smooth domain in ℝ n $$\mathbb {R}^n$$ , 1

Date: 2024
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DOI: 10.1007/978-981-99-8692-7_7

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