Moving planes, moving spheres, and a priori estimates |
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| Authors: | Wenxiong Chen Congming Li |
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| Institution: | a Department of Mathematics, Yeshiva University, New York, NY 10033, USA
b Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309, USA |
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| Abstract: | In this paper, we use the method of moving planes and the method of moving spheres to obtain a priori estimates for the solutions of semi-linear elliptic equations.Using the ‘method of moving planes’, we establish a sharper estimate on the solutions for prescribing scalar curvature equations with indefinite curvature functions and thus generalized a resent result of Lin.Applying ‘the method of moving spheres’, we give a different proof for a well-known sup+inf inequality established by Brezis, Li and Shafrir. |
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| Keywords: | Method of moving planes Moving spheres Nonlinear elliptic equations Indefinite curvature functions A priori estimates sup+inf inequalities |
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