对数各向异性Sobolev不等式

Logarithmic anisotropic Sobolev inequalities

利用Hlder不等式,分别结合各向异性Sobolev不等式和带权各向异性Sobolev不等式,得到了对数各向异性Sobolev不等式和对数带权各向异性Sobolev不等式,从而将对数Sobolev不等式推广到对数各向异性情形.

The logarithmic anisotropic Sobolev inequality is proven by using the Hlder inequality combine with the anisotropic Sobolev inequality.Furthermore,the logarithmic weighted anisotropic Sobolev inequality is obtained by the same way.It generalizes logarithmic Sobolev inequalities to the logarithmic anisotropic case.