Flows and Critical Points

Martin Schechter

Chapter Chapter 14 in Critical Point Theory, 2020, pp 243-253 from Springer

Abstract: Abstract In this chapter we study equations of the form − Δ p u = f ( x , u ) in Ω u = 0 on ∂ Ω , $$\displaystyle \begin{aligned} \left\{\begin{aligned} - {\Delta_{\mathit p}} u & = f(x,u)\;\quad && \;\text{in }\; \Omega\\ {} u & = 0 && \text{on }\; \partial{\Omega} \end{aligned}\right \}, \end{aligned}$$ where Ω is a bounded domain in ℝ n , n ≥ 1 $$\mathbb R^n,\, n \ge 1$$ , Δ p u = div ( | ∇ u | p − 2 ∇ u ) $${\Delta _{\mathit p}} u = \operatorname {\mathrm {div}} \big (|\nabla u|{ }^{p-2}\, \nabla u\big )$$ is the p-Laplacian of u, 1

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-45603-0_14

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DOI: 10.1007/978-3-030-45603-0_14

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