Optimal Rellich-Sobolev constants and their extremals. (English) Zbl 1340.46028

Musina, Roberta

Differ. Integral Equ. 27, No. 5-6, 579-600 (2014).

Summary: 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 \(\Omega\).

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10	Inequalities involving derivatives and differential and integral operators
35J57	Boundary value problems for second-order elliptic systems

Keywords:

optimal Rellich-Sobolev constant; weighted Sobolev space