期刊
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
卷 19, 期 6, 页码 2949-2964出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2020129
关键词
Singular sets; Hausdorff measure; j-symmetric; geometric structure
资金
- National Natural Science Foundation of China [11401307, 11401310, 11771214]
- Postgraduate Research & Practice Innovation Program of Jiangsu Province [KYCX17 0321]
- China Scholarship Council(CSC) [201806840122]
In this paper, we mainly investigate the classification of singular sets of solutions to elliptic equations. Firstly, we define the j-symmetric singular set S-j (u) of solution u, and show that the Hausdorff dimension of the j-symmetric singular set S-j (u) is not more than j. Then we prove the generalized epsilon-regularity lemma for j-symmetric homogeneous harmonic polynomial P with origin 0 as the isolated critical point in Rn - j, and by the generalized epsilon-regularity lemma, we show the Hausdorff measure estimate of the j-symmetric singular set S-j(u). Moreover, we study the geometric structure of interior singular points of solutions u in a planar bounded domain.
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