科研之友
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摘要
Let Omega subset of R-2 be a smooth bounded domain, and q(x) be a polynomial with q(0) not equal 0. Then under some hypothesis on q(x), there holds sup (integral Omega vertical bar del u vertical bar 2dx=1.integral Omega udx=0)integral(Omega)e(2 pi u2/q(0) q(integral Omega u2dx))dx < infinity. A sufficient condition will be given to assure that the above inequality does not hold. Furthermore, the existence of the extremal functions will be derived.
- 出版日期2009-4-15
- 单位中国人民大学
