论文标题
在RICCI曲率较低的流形和边界值问题上的流形的椭圆形系统的二次估计值
Quadratic estimates for degenerate elliptic systems on manifolds with lower Ricci curvature bounds and boundary value problems
论文作者
论文摘要
对于某些具有限制的可测量系数，（不一定要）具有正面歧管，在具有正面注射率的半径的完全歧管上，加权二次估计值已证明了具有有限的可测量系数的某些双层二阶差异算子。与早期的结果相比，RICCI曲率仅被认为是从下面界定的，并且仅假定重量在A^2中局部。在这个较弱的假设下证明了Kato Square root估计值。在紧凑的Lipschitz歧管上，我们证明了对溶液的溶解性估算值，该解决方案不一定是自相关系数的退化椭圆系统，以及Dirichlet，Neumann和Atiyah-Patodi-Serger边界条件。
Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius. As compared to earlier results, Ricci curvature is only assumed to be bounded from below, and the weight is only assumed to be locally in A^2. The Kato square root estimate is proved under this weaker assumption. On compact Lipschitz manifolds we prove solvability estimates for solutions to degenerate elliptic systems with not necessarily self-adjoint coefficients, and with Dirichlet, Neumann and Atiyah-Patodi-Singer boundary conditions.
