| Abstract: |
| In this talk our main interest is to analyze how the geometry of boundary singularity can affect the existence of positive solutions of elliptic equations. In particular, we consider the existence of a positive solution to the semilinear elliptic equation involving the Sobolev critical term and the Hardy critical terms with multiple singularities on the boundary. Meanwhile, we show the existence of minimizers for the Caffarelli-Kohn-Nirenberg inequalities when N = 3 -this solves the problem left open in [Chern-Lin,Arch. Arch. Rational Mech. Anal., 2010], hence completing a long line of research. |
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