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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
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