Differential and Integral Equations

Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature

Ali Hyder

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this article, we study the nonlocal equation $$ (-\Delta)^{\frac{n}{2}}u=(n-1)!e^{nu}\quad \text{in $\mathbb R$}, \quad\int_{\mathbb R}e^{nu}dx < \infty, $$ which arises in the conformal geometry. Inspired by the previous work of C.S. Lin and L. Martinazzi in even dimension and T. Jin, A. Maalaoui, L. Martinazzi, J. Xiong in dimension three, we classify all solutions to the above equation in terms of their behavior at infinity.

Article information

Source
Differential Integral Equations, Volume 32, Number 7/8 (2019), 423-454.

Dates
First available in Project Euclid: 2 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1556762424

Mathematical Reviews number (MathSciNet)
MR3945763

Subjects
Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 53A30: Conformal differential geometry 35R11: Fractional partial differential equations

Citation

Hyder, Ali. Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature. Differential Integral Equations 32 (2019), no. 7/8, 423--454. https://projecteuclid.org/euclid.die/1556762424


Export citation