Best constants in Sobolev and Gagliardo–Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations
Best constants in Sobolev and Gagliardo–Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations
Abstract In this paper the dependence of the best constants in Sobolev and Gagliardo–Nirenberg inequalities on the precise form of the Sobolev space norm is investigated. The analysis is carried out on general graded Lie groups, thus including the cases of $$\mathbb {R}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:math> , Heisenberg, and general stratified …