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The method of moving planes for integral equations and a regularity lifting lemma
PDE Seminar| Speaker: | Professor Congming Li, University of Colorado at Boulder |
| Location: | 693 Kerr |
| Start time: | Thu, Oct 13 2005, 3:10PM |
I will present the recent work (joint with W. Chen, C. Jin, J. Lim, and B. Ou) on systems of integral equations related to the Hardy-Littlewood-Sobolev (HLS) inequality. The focus is on the Euler-Lagrange equations of the HLS. These equations have been the focal point in the field of analysis of nonlinear elliptical PDEs including the Yamabe problem and the Nirenberg problem. We study the symmetry, monotonicity, regularity and the asymptotic of the solutions. I will introduce some key futures of the main technique--the method of moving planes for integral equations and will also present a simple method for the study of regularity and obtain the optimal integrability interval for solutions of a class of systems equations as an application. The later is the key for us to obtain the exact asymptotic of the solutions.