Concentration of solutions of non-linear elliptic equations involving critical Sobolev exponent

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Abstract

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.

Keywords

concentration , blow-up , scalar curvature equation
  • Man Chun Leung Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. Republic of Singapore.
  • Pages: 1–21
  • Date Published: 2005-04-01
  • Vol. 7 No. 1 (2005): CUBO, A Mathematical Journal

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Published

2005-04-01

How to Cite

[1]
M. Chun Leung, “Concentration of solutions of non-linear elliptic equations involving critical Sobolev exponent”, CUBO, vol. 7, no. 1, pp. 1–21, Apr. 2005.

Issue

Vol. 7 No. 1 (2005): CUBO, A Mathematical Journal

Section

Articles