zbMATH — the first resource for mathematics

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