Minimization of quotients with variable exponents

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 $j\to \infty$ and after when $l\to \infty .$

29 pages

References in corpus (1)

• Asymptotics for the best Sobolev constants and their extremal functions