Quantitative analysis of some system of integral equations |
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Authors: | Chao Jin Congming Li |
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Affiliation: | (1) Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO 80309, USA |
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Abstract: | In this paper, we study the integrability of the non-negative solutions to the Euler-Lagrange equations associated with Weighted Hardy-Littlewood-Sobolev (HLS) inequality. We obtain the optimal integrability for the solutions. The integrability and the radial symmetry (which we derived in our earlier paper) are the key ingredients to study the growth rate at the center and the decay rate at infinity of the solutions. These are also the essential properties needed to classify all non-negative solutions. Some simple generalizations are also provided here. |
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Keywords: | Weighted Hardy-Littlewood-Sobolev inequalities Integral equations and systems Radial symmetry Monotonicity Moving planes in integral forms |
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