JournalsaihpcVol. 38, No. 4pp. 1167–1216

Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities

  • Tianling Jin

    Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
  • Jingang Xiong

    School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, Beijing 100875, China
Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities cover
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Abstract

We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension of the celebrated theorem of Caffarelli-Gidas-Spruck for the second order Yamabe equation with isolated singularities to higher order equations. Our approach uses blow up analysis for local integral equations, and is unified for all critical elliptic equations of order smaller than the dimension. We also prove the existence of Fowler solutions to the global equations, and establish a sup ⁎ inf type Harnack inequality of Schoen for integral equations.

Cite this article

Tianling Jin, Jingang Xiong, Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1167–1216

DOI 10.1016/J.ANIHPC.2020.10.005