## Differential and Integral Equations

### Optimal Rellich-Sobolev constants and their extremals

Roberta Musina

#### Abstract

We prove that extremals for second order Rellich-Sobolev inequalities have a constant sign. Then, we show that the optimal constants in Rellich-Sobolev inequalities on a bounded domain $\Omega$ and under Navier boundary conditions do not depend on $\Omega$.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 5/6 (2014), 579-600.

Dates
First available in Project Euclid: 3 April 2014