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On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates

Ivan Hlaváček, Michal Křížek (1987)

Aplikace matematiky

Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order O ( h 2 ) are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang (2016)

Annales Polonici Mathematici

This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that ̅ ω k = 0 for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle K X - 1 is nef, then for any ε >...

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