Differential and Integral Equations

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

Ali Hyder

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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

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

First available in Project Euclid: 2 May 2019

Permanent link to this document

Mathematical Reviews number (MathSciNet)

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


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

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