Doubling annulus Pohožaev type identity and applications to approximate biharmonic maps.
- Resource Type
- Article
- Authors
- Chen, Youmin; Zhu, Miaomiao
- Source
- Calculus of Variations & Partial Differential Equations. Jan2024, Vol. 63 Issue 1, p1-25. 25p.
- Subject
- *RIEMANNIAN manifolds
- Language
- ISSN
- 0944-2669
We derive a refined doubling annulus Pohožaev type identity for approximate extrinsic biharmonic maps from a general Riemannian 4-manifold into a compact Riemannian manifold. As applications, we show a compactness result modular finitely many bubbles for a sequence of such maps with finite biharmonic energy and with tension fields uniformly bounded in L p for some p ≥ 8 7 . Also, we derive the convergence behavior and the existence of finite time singularities of the biharmonic map heat flow from a general Riemannian 4-manifold into a compact Riemannian manifold. [ABSTRACT FROM AUTHOR]