Regularity for weakly (<italic>K</italic><sub>1</sub>,<italic>K</italic><sub>2</sub>(<italic>x</italic>))-quasiregular mappings of several <italic>n</italic>-dimensional variables

Hongya GAO; Qiuhua HUANG; Fang QIAN

doi:10.1007/s11464-011-0093-1

PDF(173 KB)

Front. Math. China ›› 2011, Vol. 6 ›› Issue (2) : 241-251. DOI: 10.1007/s11464-011-0093-1

RESEARCH ARTICLE

Regularity for weakly (K₁,K₂(x))-quasiregular mappings of several n-dimensional variables

Author information +

History +

Abstract

The definition for weakly (K₁,K₂(x))-quasiregular mappings of several n-dimensional variables is given. A regularity property is obtained by using the stability result of Hodge decomposition, some analytical tools of Sobolev spaces, and differential geometry, which can be regarded as a generalization of the results due to T. Iwaniec and Hongya Gao.

Keywords

Weakly (K₁ / K₂(x))-quasiregular mapping of several n-dimensional variables / weak reverse Hölder inequality / regularity

Cite this article

EndNote

Ris (Procite)

Bibtex

Download citation ▾

Hongya GAO, Qiuhua HUANG, Fang QIAN. Regularity for weakly (K₁,K₂(x))-quasiregular mappings of several n-dimensional variables. Front Math Chin, 2011, 6(2): 241‒251 https://doi.org/10.1007/s11464-011-0093-1

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Dairbekov N S. The concept of a quasiregular mapping of several n-dimensional variables. Dokl. RAN, 1992, 423(3): 511-514

[2]	Dairbekov N S. Quasiregular mappings of several n-dimensional variables. Siberian Mathematical Journal, 1993, 34(4): 87-102 CrossRef Google scholar

[3]	Dairbekov N S. Stability of classes of quasiregular mappings in several spatial variables. Siberian Mathematical Journal, 1995, 36(1): 43-54 CrossRef Google scholar

[4]	Donalson S K, Sullivan D P. Qasiconformal conformal 4-manifolds. Acta Math, 1989, 163: 181-252

[5]	Gao Hongya. Regularity for weakly (K₁,K₂)-quasiregular mappings. Sci in China, Ser A, 2003, 46(4): 499-505

[6]	Gao Hongya, Li Tong. On degenerate weakly (K₁,K₂)-quasiregular mappings. Acta Math Sci, 2008, 28B(1): 163-170 CrossRef Google scholar

[7]	Gao Hongya, Liu Haihong, Zhou Shuqing. Higher integrability for weakly (K₁,K₂(x))-quasiregular mappings. Acta Math Sin, 2009, 52(5): 847-852 (in Chinese)

[8]	Gao Hongya, Zhou Shuqing, Meng Yuqin. A new inequality for weakly (K₁,K₂)-quasiregular mappings. Acta Math Sin (Eng Ser), 2007, 23(12): 2241-2246 CrossRef Google scholar

[9]	Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Ann of Math Stud, 105. Princeton: Princeton Univ Press, 1983

[10]	Iwaniec T. p-harmonic tensors and quasiregular mappings. Ann of Math, 1992, 136(3): 589-624 CrossRef Google scholar

[11]	Iwaniec T, Martin G. Quasiregular mappings in even dimensions. Acta Math, 1993, 170: 29-81 CrossRef Google scholar

[12]	Iwaniec T, Martin G. Geometric Function and Non-linear Analysis. Oxford: Clarendon Press, 2001

[13]	Iwaniec T, Sbordone C. On the integrability of the Jacobian under minimal hypotheses. Arch Rational Mech Anal, 1992, 119: 129-143 CrossRef Google scholar