Symmetry of solutions to some systems of integral equations

By Chaosong Jin, Congming LI #. 2005

89 citations recorded by the source corpus.

In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we established the radial symmetry of the solutions to the Euler-Lagrange equations associated with the classical and weighted Hardy-Littlewood-Sobolev inequality.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/8fcf527603e1f9847d873d5755360b81b8c0d4d9

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In Applied Mathematics

1. Congming LI #
2. L. D’Ambrosio
3. Wenxiong CHEN *
4. Yutian Lei
5. Enzo Mitidieri
6. Chao Ma
7. G. Caristi
8. Li Ma

Citations in the corpus

• Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy–Littlewood–Sobolev system of integral equations (2012, background): “’s work, Jin and Li [13] studied the symmetry of the solutions to the more general system of integral equations (1.”
• Symmetry and regularity of extremals of an integral equation related to the Hardy–Sobolev inequality (2011, unknown): “2 The proof of Theorem 1 For the convenience of the reader, we present the following Weighted Hardy–Littlewood– Sobolev inequality (see [16]).”
• Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, methodology): “There are many more applications of this method to integral systems, and the interested readers may see [10] [12] [15] [20] [21] [28] [33] [34] [40] [42] [45] [46] [47] [50] [53] [54] and the references therein.”
• Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems (2008, methodology): “2) and the integrability condition (u, v) ∈ L(R )×L(R ), solutions of this problem are rescaled optimizers of the well known Hardy-LittlewoodSobolev inequality (see for instance [3, 4, 13, 14]), ∣∣∣∣ ∫ RN ∫”
• Liouville type theorems for integral equations and integral systems (2013, unknown): “in [9] and [10] and then used widely in [6,8,17–19,23–26].”