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- Title
Subgradient estimates for a nonlinear subparabolic equation on complete pseudo-Hermitian manifolds.
- Authors
Wu, Wenjing
- Abstract
Let (M , J , θ) be a complete noncompact pseudo-Hermitian manifold which satisfies the CR sub-Laplacian comparison property. We first obtain local subgradient estimates for positive solutions to the following nonlinear subparabolic equation: u t = Δ b u + a u ln u + b u , on M × [ 0 , + ∞) , where a, b are two real constants. As a application, we derive a priori estimate for positive solutions to the subelliptic equation Δ b u + a u ln u = 0 . Secondly, we deform the pseudo-Hermitian form by the general CR flow on a complete noncompact pseudo-Hermitian 3-manifold. We show that if a pseudo-Hermitian form evolves, then we have a new local subgradient estimate for positive solutions to the equation u t = Δ b u + a u ln u + b u .
- Subjects
NONLINEAR equations; HERMITIAN forms; PARABOLIC operators; A priori
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-024-02689-6