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- W2757833870 abstract "In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes the cases of $mathbb R^n$, Heisenberg, and general stratified Lie groups. As an application, using the critical Gagliardo-Nirenberg inequality the existence of least energy solutions of nonlinear Schrodinger type equations is obtained. We also express the best constant in the critical Gagliardo-Nirenberg and Trudinger inequalities in the variational form as well as in terms of the ground state solutions of the corresponding nonlinear subelliptic equations. The obtained results are already new in the setting of general stratified groups (homogeneous Carnot groups). Among new technical methods, we also extend Folland's analysis of Holder spaces from stratified groups to general homogeneous groups." @default.
- W2757833870 created "2017-10-06" @default.
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- W2757833870 date "2017-09-24" @default.
- W2757833870 modified "2023-09-26" @default.
- W2757833870 title "Critical Sobolev, Gagliardo-Nirenberg, Trudinger and Brezis-Gallouet-Wainger inequalities, best constants, and ground states on graded groups" @default.
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