Gradient estimate and universal bounds for semilinear elliptic equations on RCD * (K,N) metric measure spaces
Abstract
We derive logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on RCD∗(K,N) metric measure spaces, which contains the class of Riemannian manifolds with Ricci curvature bounded below. These estimates are applicable for equations satisfying subcritical index condition, which recover many classical results even on Euclidean spaces. In certain case, these estimates are optimal even on RCD∗(K,N) spaces with K1.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Communications in Partial Differential Equations
- Publisher
- Informa UK Limited
- Volume
- 51
- Issue
- 2-3
- Pages
- 273–313
- Publication date
- 4 March 2026
- Language
- EN