Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs

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• 作者：Nguyen Lam ; Guozhen Lu ; Hanli Tang
• 关键词：Subcritical Moser&ndash ; Trudinger inequality ; Heisenberg group ; Sharp constants ; Q-Laplace on the Heisenberg group ; Nonlinear subelliptic equations ; Exponential growth ; Existence of solutions
• 刊名：Nonlinear Analysis
• 出版年：January, 2014
• 年：2014
• 卷：95
• 期：Complete
• 页码：77-92
• 全文大小：459 K

文摘

sup鈥栤垏Hu鈥朙Q(H)鈮?1鈥杣鈥朙Q(H)Q鈭捨测埆H1蟻(尉)尾{exp(伪|u|Q/(Q鈭?))鈭掆垜k=0Q鈭?伪kk!|u|kQ/(Q鈭?)}鈮伪,尾.In contrast to the analogous inequality in Euclidean spaces proved in Adachi and Tanaka (1999) using symmetrization, our argument is completely different and avoids the symmetrization method which is not available on the Heisenberg group in an optimal way. Moreover, our restriction on the norm of the function is much weaker than which was assumed in Lam and Lu (2012) . As a consequence, our inequality fails at in contrast to the one in .(0.1)鈭捨擰u+V(尉)|u|Q鈭?u=f(尉,u)蟻(尉)尾 聽in聽 H