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Weighted quadratic estimates are proved for certain bisectorial firstorderdifferential operators with bounded measurable coefficients which are (notnecessarily pointwise) accretive, on complete manifolds with positiveinjectivity radius. As compared to earlier results, Ricci curvature is onlyassumed to be bounded from below, and the weight is only assumed to be locallyin A^2. The Kato square root estimate is proved under this weaker assumption.On compact Lipschitz manifolds we prove solvability estimates for solutions todegenerate elliptic systems with not necessarily self-adjoint coefficients, andwith Dirichlet, Neumann and Atiyah-Patodi-Singer boundary conditions.

Quadratic estimates for degenerate elliptic systems on manifolds with lower Ricci curvature bounds and boundary value problems