The effects of a discontinues weight for a problem with a critical nonlinearity

2014/05/29 by Rejeb Hadiji, Hadiji, Rejeb, Sami Baraket +3
Computer Science · Mathematics · #35H30 #35J20 #35J25 #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1405.7734

openalex publication_date 2014/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the minimizing problem inf\∫_Ωp(x)|∇ u|²dx, u∈ H¹₀(Ω), ‖u‖_{L^(2N)/(N-2)(Ω)}=1\ where Ω is a smooth bounded domain of \R^N, N≥ 3 and p a positive discontinuous function. We prove the existence of a minimizer under some assumptions.

Citations

• A relation between pointwise convergence of functions and convergence of functionals

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