对称Sobolev空间到加权L^(2^*)空间的紧嵌入

Compact Embedding of Symmetric Sobolev Spaces to Weighted L^(2^*) Spaces

根据LIons引理,建立了Sobolev空间H1(Rn)到一类加权L2*空间紧嵌入定理。将这一理论应用到Rn上的标量场方程,得到具有限能量的正解,推广了文献[2]的部分结果。

Symmetric Sobolev spaces, consisted of radially symmetric functions of first Sobolev spaces, can be embedded compactly into weighted L^2^＊ spaces under proper weight. As an application,finite energy solutions are obtained for a class of scalar field equations.