Title：On the minimizers of Caffarelli-Kohn-Nirenberg inequality in
three dimension
Abstract: The minimizer of a functional inequality is often hard to find, and the minimizer of the famous Sobolev inequality are the least-energy solutions of the Yamabe equation in the Euclidean space, which can be viewed as the Euler-Lagrange equation for the Sobolev inequality. There is a far-reaching generalization of the Sobolev inequality by Caffarelli-Kohn-Nirenberg which includes also the Hardy inequality as a special case. The minimizer problem for CKN is solved except for the boundary-singular case in three dimension. We will show how to solve this problem in this talk. The existence of the minimizer is reduced to solving the Yamabe equation with a Hardy singularity.
时间：2014年4月4日 14:00-15:00
地点：3B207
方向教授, 1978年出生，1998年本科毕业于北京大学，2002年于美国Texa A&M 大学获得博士学位，现任教于国立中央大学。目前主要从事算子理论，调和分析，偏微分方程相关方面的研究。科研成果均发表在GAFA, Math.Res.Lett. Adv.Math. J.Rein.Angew.Math. J.Funct.Anal 等数学期刊上。
