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A lusin type theorem for gradients

✍ Scribed by Giovanni Alberti


Book ID
107795067
Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
361 KB
Volume
100
Category
Article
ISSN
0022-1236

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In this paper, we derive a Liouville type theorem on a complete Riemannian manifold without boundary and with nonnegative Ricci curvature for the equation \(\Delta u(x)+h(x) u(x)=0\), where the conditions \(\lim _{r \rightarrow x} r^{-1} \cdot \sup _{x \in B_{p}(r)}|\nabla h(x)|=0\) and \(h \geqslan

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It is discussed that the derivation of different SCF-type equations through the relevant (generalized) Brillouin theorems can be utilized to obtain the energy gradients of the method studied. This is illustrated for the case of the UHF method and used to obtain the gradient formula applicable in the