A Class of Sub-elliptic Equations on the Heisenberg Group and Related Interpolation Inequalities

作者: Jianqing Chen , Eugénio M. Rocha

DOI: 10.1007/978-3-0348-0516-2_7

关键词:

摘要: We firstly prove the existence of least energy solutions to a class sub–elliptic equations on Heisenberg group. Then we use this solution give sharp estimate smallest positive constant in Gagliardo–Nirenberg inequality Finally point out some extensions quasilinear case.

参考文章(28)
Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei V. Rogosin, Multi-index Mittag-Leffler Functions Springer Monographs in Mathematics. pp. 129- 164 ,(2014) , 10.1007/978-3-662-43930-2_6
Ermanno Lanconelli, Francesco Uguzzoni, Andrea Bonfiglioli, Stratified Lie groups and potential theory for their sub-Laplacians ,(2007)
E. Lanconelli, N. Garofalo, Existence and nonexistence results for semilinear equations on the Heisenberg group Indiana University Mathematics Journal. ,vol. 41, pp. 71- 98 ,(1992)
Isabeau Birindelli, Alessandra Cutrì, A semi-linear problem for the Heisenberg laplacian Rendiconti del Seminario Matematico della Università di Padova. ,vol. 94, pp. 137- 153 ,(1995)
Alexander Meskhi, Vakhtang Kokilashvili, Lars-Erik Persson, Weighted Norm Inequalities for Integral Transforms With Product Kernals ,(2013)
Lech Maligranda, Natan Ya. Krugljak, Irina U. Asekritova, Lars-Erik Persson, Distribution and rearrangement estimates of the maximal function and interpolation Studia Mathematica. ,vol. 124, pp. 107- 132 ,(1997)
Lars-erik Persson, Alois Kufner, Natasha Samko, Weighted Inequalities Of Hardy Type ,(2003)
L.-E. Persson, V. D. Stepanov, E. P. Ushakova, Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions Proceedings of the American Mathematical Society. ,vol. 134, pp. 2363- 2372 ,(2006) , 10.1090/S0002-9939-06-08403-6
E Lanconelli, F Uguzzoni, Non-existence results for semilinear kohn-laplace equations in unbounded domains Communications in Partial Differential Equations. ,vol. 25, pp. 1703- 1739 ,(2000) , 10.1080/03605300008821564
E. Sawyer, Boundedness of classical operators on classical Lorentz spaces Studia Mathematica. ,vol. 96, pp. 145- 158 ,(1990) , 10.4064/SM-96-2-145-158