Differential and Integral Equations

Optimal Rellich-Sobolev constants and their extremals

Roberta Musina

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1396558098

Mathematical Reviews number (MathSciNet)
MR3189533

Zentralblatt MATH identifier
1340.46028

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 26D10: Inequalities involving derivatives and differential and integral operators 35J55

Citation

Musina, Roberta. Optimal Rellich-Sobolev constants and their extremals. Differential Integral Equations 27 (2014), no. 5/6, 579--600. https://projecteuclid.org/euclid.die/1396558098


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