Concentration of solutions of non-linear elliptic equations involving critical Sobolev exponent
Chun Leung, Man
In IRn (n ≥ 3), an interesting property of the semi-linear equation Is that, when K0 is a positive constant, solutions can concentrate at any point. When K0 is not a constant, we show that concentration of solutions requires strong conditions on K0. Through the stereographic projection, the discussion can be extended to Sn, and is related to bubbling, or the blow-up phenomenon.