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Volume 32, Issue 1
Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group

Xinjing Wang & Pengcheng Niu

DOI: 10.4208/jpde.v32.n1.5

J. Part. Diff. Eq., 32 (2019), pp. 66-76.

Published online: 2019-04

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  • Abstract

The aim of the paper is to study properties of solutions to the nonlinear fractional subLaplace equations on the Heisenberg group. Based on the method of moving planes to the Heisenberg group, we prove the Liouville property of solutions on a half space and the symmetry and monotonicity of the solutions on the whole group respectively.

  • Keywords

Heisenberg group fractional subLaplace equation method of moving planes.

  • AMS Subject Headings

35A01, 35J57, 35D99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shingw@sina.com (Xinjing Wang)

pengchengniu@nwpu.edu.cn (Pengcheng Niu)

  • BibTex
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  • TXT
@Article{JPDE-32-66, author = {Wang , Xinjing and Niu , Pengcheng}, title = {Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {1}, pages = {66--76}, abstract = {

The aim of the paper is to study properties of solutions to the nonlinear fractional subLaplace equations on the Heisenberg group. Based on the method of moving planes to the Heisenberg group, we prove the Liouville property of solutions on a half space and the symmetry and monotonicity of the solutions on the whole group respectively.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/13123.html} }
TY - JOUR T1 - Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group AU - Wang , Xinjing AU - Niu , Pengcheng JO - Journal of Partial Differential Equations VL - 1 SP - 66 EP - 76 PY - 2019 DA - 2019/04 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/13123.html KW - Heisenberg group KW - fractional subLaplace equation KW - method of moving planes. AB -

The aim of the paper is to study properties of solutions to the nonlinear fractional subLaplace equations on the Heisenberg group. Based on the method of moving planes to the Heisenberg group, we prove the Liouville property of solutions on a half space and the symmetry and monotonicity of the solutions on the whole group respectively.

Wang , Xinjing and Niu , Pengcheng. (2019). Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group. Journal of Partial Differential Equations. 32 (1). 66-76. doi:10.4208/jpde.v32.n1.5
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