关于Sobolev空间的等价模定理的一个证明

Sobolev space on the equivalent modulus of a theorem proved

Sobolev空间的等价模定理是现代数学理论研究的重要工具,利用Sobolev嵌入定理和Poincar不等式定义Sobolev空间上的一个结构更为简单的新范数,并证明了其与原范数的等价性.

The theorem of the equivalence of norms for class of Sobolev space has been an important fool to study modern theory of mathematics.In this paper,A new norm that has the simple structure is definted using the Sobolev imbedding theorem and the Poincaré inequality,and the equivalence with the before norm is proved.