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arXiv · 1706.05590

Minimization of quotients with variable exponents

Claudianor O. Alves·Mario Daniel H. Bolaños·Grey Ercole
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Abstract

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, $p\in C^{1}(\overline{\Omega}),$ $q\in C(\overline{\Omega})$ and $l,j\in\mathbb{N}.$ We describe the asymptotic behavior of the minimizers of the Rayleigh quotient $\frac{\Vert\nabla u\Vert_{lp(x)}}{\Vert u\Vert_{jq(x)}}$, first when $j\rightarrow\infty$ and after when $l\rightarrow\infty.$

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Claudianor O. Alves, Mario Daniel H. Bolaños, Grey Ercole. 2017-06-17. Minimization of quotients with variable exponents. https://doi.org/10.1016/j.jde.2018.04.010

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