Nonstandard growth optimization problems with volume constraint

2021/07/28 by Ariel Salort, Salort, Ariel, Belem Schvager +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.13596

openalex publication_date 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study some optimal design problems related to nonstandard growth eigenvalues ruled by the g-Laplacian operator. More precisely, given Ω⊂ \Rⁿ and α,c>0 we consider the optimization problem inf \ λ_Ω(α,E)\colon E⊂ Ω, |E|=c \, where λ_Ω(α,E) is related to the first eigenvalue to -div(g( |∇ u |)\tfrac∇ u|∇ u|) + g(u)\tfracu|u|+ αχ_E g(u)\tfracu|u| in Ω subject to Dirichlet, Neumann or Steklov boundary conditions. We analyze existence of an optimal configuration, symmetry properties of them, and the asymptotic behavior as α approaches +∞.

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