We study the solutions $uin C^infty( n)$ of the problem egin{equation}label{P0} (-Delta)^mu=ar Qe^{2mu}, ext{ where }ar Q=pm (2m-1)!, quad V :=int_{ n}e^{2mu}dx 1$. Problem eqref{P0} corresponds to finding conformal metrics $g_u:=e^{2u}|dx|^2$ on $ n$ with constant $Q$-curvature $ar Q$ and finite volume $V$. Extending previous works of Chang-Chen, and Wei-Ye, we show that both the value $V$ and the asymptotic behavior of $u(x)$ as $|x| o infty$ can be simultaneously prescribed, under certain restrictions. When $ar Q= (2m-1)!$ we need to assume $V
Conformal metrics on R2m with constant Q-curvature, prescribed volume and asymptotic behavior / Hyder, Ali; Martinazzi, Luca. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 35:1(2015), pp. 283-299. [10.3934/dcds.2015.35.283]
Conformal metrics on R2m with constant Q-curvature, prescribed volume and asymptotic behavior
Martinazzi, Luca
2015
Abstract
We study the solutions $uin C^infty( n)$ of the problem egin{equation}label{P0} (-Delta)^mu=ar Qe^{2mu}, ext{ where }ar Q=pm (2m-1)!, quad V :=int_{ n}e^{2mu}dx 1$. Problem eqref{P0} corresponds to finding conformal metrics $g_u:=e^{2u}|dx|^2$ on $ n$ with constant $Q$-curvature $ar Q$ and finite volume $V$. Extending previous works of Chang-Chen, and Wei-Ye, we show that both the value $V$ and the asymptotic behavior of $u(x)$ as $|x| o infty$ can be simultaneously prescribed, under certain restrictions. When $ar Q= (2m-1)!$ we need to assume $VI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
