| Abstract: |
| We consider on compactness for the embedding from radial Sobolev spaces $W^{1,p}_{rad}(\mathbf{R}^N)$ to variable exponent Lebesgue spaces $L^{q(x)}(\mathbf{R}^N)$. In particular, we point out that the behavior of $q(x)$ at infinity plays an essential role on compactness. As an application we prove the existence of solutions of the quasi-linear elliptic equation with a variable critical exponent. This is a joint work with Masato Hashizume (Ehime University). |
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