Photo from archive.org
In this short note, we study the prescribed Q-curvature equation with a singularity at the origin in $${\mathbb {R}}^4$$ , namely, $$\begin{aligned} \Delta ^2u=(1-|x|^p)e^{4u}-c\delta _0\quad \text {in}\quad {\mathbb {R}}^4 \end{aligned}$$… Click to show full abstract
In this short note, we study the prescribed Q-curvature equation with a singularity at the origin in $${\mathbb {R}}^4$$ , namely, $$\begin{aligned} \Delta ^2u=(1-|x|^p)e^{4u}-c\delta _0\quad \text {in}\quad {\mathbb {R}}^4 \end{aligned}$$ under a finite volume condition, where $$p>0$$ and $$c\in {\mathbb {R}}$$ . We prove the nonexistence of normal solutions to the above equation. This partly generalizes the nonexistence results of Hyder and Martinazzi ( arXiv:2010.08987 , 2020) where $$c=0$$ , and extends the conclusion of Hyder et al. (Int Math Res Not, 2019. https://doi.org/10.1093/imrn/rnz149 ) where $$p=0$$ .
Journal Title: Archiv der Mathematik
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!