No abstract

In this paper, we prove several inequalities such as Sobolev, Poincaré, logarithmic Sobolev, which involve a general norm with accurate information of extremals, and are valid for some symmetric functions. We use Ioku's transformation, which is a special case of p-harmonic transplantation, between symmetric functions.

<p style='text-indent:20px;'>In this paper we are concerned with the least energy solutions to the Lane-Emden problem driven by an anisotropic operator, so-called the Finsler <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula>-Laplacian, on a bounded domain in <inline-formula><tex-math id="M2">\begin{document}$ {\mathbb{R}}^N $\end{document}</tex-math></inline-formula>. We prove several asymptotic formulae as the nonlinear exponent gets large.</p>

In this paper we are concerned with the least energy solutions to the Lane-Emden problem driven by an anisotropic operator, so-called the Finsler N -Laplacian, on a bounded domain in R N . We prove several asymptotic formulae as the nonlinear exponent gets large.