In this article we obtain a priori estimates for solutions to the prescribed scalar curvature equation on 2- and 3-spheres under a nondegeneracy assumption on the curvature function. Using this estimate, we use the continuity method to demonstrate the existence of solutions to this equation when a map associated to the given curvature function has non-zero degree.
|Original language||English (US)|
|Number of pages||25|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - May 1993|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Mathematics subject classifications: 35J60, 58G03