Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations

摘要: In this paper the dependence of best constants in Sobolev and Gagliardo-Nirenberg inequalities on precise form space norm is investigated. The analysis carried out general graded Lie groups, thus including cases $\mathbb R^n$, Heisenberg, more stratified groups. norms may be defined terms Rockland operators, i.e. hypoelliptic homogeneous left-invariant differential operators group. are expressed variational as well ground state solutions corresponding nonlinear subelliptic equations. orders these equations can high depending order or inequalities, fractional. Applications obtained also to with lower given by different operators. Already case results extend classical relations Weinstein a wide range elliptic low interpolation type. However, proofs from those ivy because impossibility using rearrangement already setting Heisenberg considered class groups most nilpotent where one still consider invariant