On the compactness theorem for differential forms

V. I. Kuzminov; I. A. Shvedov

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On the compactness theorem for differential forms

机译：关于微分形式的紧性定理

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Kichenassamy found conditions under which the space W_p~k of differential forms on a closed manifold M with the norm ‖ω‖_(W_p) = ‖ω‖_(L_p) + ‖dω‖_(L_p) embeds compactly in the space F_p~k of currents on M with the norm inf_(α∈L_p) {‖ω - dα‖_(L_q) + ‖α‖_(L_q)}. We give a version of Kichenassamy's theorem for an arbitrary Banach complex and, in particular, for an elliptic differential complex on a closed manifold.

机译：Kichenassamy找到了条件，其中范数为“ω” _（W_p）=“ω” _（L_p）+“dω” _（L_p）的闭合流形M上的微分形式空间W_p〜k紧凑地嵌入空间F_p M上具有范数inf_（α∈L_p）{‖ω-dα‖_（L_q）+‖α‖_（L_q）}的〜k个电流。对于任意Banach复数，特别是在封闭流形上的椭圆微分复数，我们给出了Kichenassamy定理的一个版本。

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《Siberian Mathematical Journal》 |2003年第1期|共8页
作者
V. I. Kuzminov; I. A. Shvedov;
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正文语种 eng
中图分类数学;
关键词
embedding theorem; Sobolev space; Banach complex; elliptic differential complex; reflexive subcategory;

机译：嵌入定理;Sobolev空间;Banach复合体;椭圆微分复合体;反身子类别;

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On the compactness theorem for differential forms

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