Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
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| Institution: | 1. Department of Mathematics, Federal University of Paraíba, 58051-900, João Pessoa-PB, Brazil;2. Department of Mathematics, Brasília University, 70910-900, Brasília, DF, Brazil;3. Department of Mathematics, Federal University of Sergipe, 49100-000, São Cristovão-SE, Brazil;1. Université Côte d''Azur, Inria, CNRS, LJAD, France;2. Université de Bourgogne, Institut de Mathématiques de Bourgogne, France;1. School of Science and Technology, University of New England, Armidale, NSW 2351, Australia;2. Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo 164-8525, Japan;3. School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, PR China;1. Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria;2. Department of Mathematics, University of Houston, Houston, TX 77204, USA;1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA;2. Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea |
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| Abstract: | We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a rotationally symmetric Fowler type solution. This result generalizes the celebrated work due to Caffarelli, Gidas and Spruck 1] who studied asymptotic proprieties to the classic Yamabe equation. In addition, we generalize similar results by Marques 12] for inhomogeneous context, that is, when the metric is not necessarily conformally flat. |
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| Keywords: | Critical equations Elliptic systems Asymptotic symmetry Singular solution A priori estimate |
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