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arXiv 2107.13596math.AP
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带体积约束的非标准增长最优化问题

Nonstandard growth optimization problems with volume constraint

Ariel Salort, Belem Schvager, Analía Silva

备注：
the definition of eigenvalue was clarified
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摘要：

本文研究了与$g-$ Laplacian算子控制的非标准增长特征值有关的优化设计问题。更确切地说，给定$Ω\subset \R^n$和$α,c>0$，我们考虑最优化问题$\inf \{ λ_Ω(α,E)\colon E\subset Ω, |E|=c \}$，其中$λ_Ω(α,E)$与$$ -\text{div}(g( |\nabla u |)\tfrac{\nabla u}{|\nabla u|}) + g(u)\tfrac{u}{|u|}+ αχ_E g(u)\tfrac{u}{|u|} \quad \text{ in }Ω$$的第一特征值有关，服从Dirichlet，Neumann或Steklov边界条件。分析了最优构型的存在性、对称性以及$α$逼近$+\infty$的渐近行为.

英文摘要：

In this article we study some optimal design problems related to nonstandard growth eigenvalues ruled by the $g-$Laplacian operator. More precisely, given $Ω\subset \R^n$ and $α,c>0$ we consider the optimization problem $\inf \{ λ_Ω(α,E)\colon E\subset Ω, |E|=c \}$, where $λ_Ω(α,E)$ is related to the first eigenvalue to $$ -\text{div}(g( |\nabla u |)\tfrac{\nabla u}{|\nabla u|}) + g(u)\tfrac{u}{|u|}+ αχ_E g(u)\tfrac{u}{|u|} \quad \text{ in }Ω$$ 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 $+\infty$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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