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Weak Differentiability of Solutions for Nonlinear Sub-elliptic Equations in the Heisenberg Group(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2003年05期
Page:
647-652
Research Field:
Publishing date:

Info

Title:
Weak Differentiability of Solutions for Nonlinear Sub-elliptic Equations in the Heisenberg Group
Author(s):
YangXiaoping ZhaoPeibiao
School of Sciences,NUST,Nanjing 210094
Keywords:
sub-ellipt ics Heisenberg g roup w eak differentiability
PACS:
O175.2
DOI:
-
Abstract:
With the help of f ract ional dif ference quot ient s, the W 2, 2 -w eak differentiability of solut ions for a nonlinear sub-elliptic equat ion in the Heisenberg group is established. This is a g eneralizat ion of theory for part ial differential equat ions in Euclidean spaces to that of general met ric spaces. There are many important applicat ions in geometrical cont rol theory and mathemat ical physics.

References:

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2 Folland G, Stein E M. Har dy spaces on homogeneous gr oups[M] . Princeton: Pr inceto n University Press, 1982.
3 Koranyi A, Reimann H M. Foundat ions for the theory of quasiconformal mappings on the Heisenberg g roup[ J] . Adv Math, 1995, 111( 1) : 1~ 87.
4 Montg omer y R. A tour of sub- riemannian geometr ies, t heir geodesic and applications, AMS, Vol 91, [ M] . Providence: AMS Math Surveys and Monograhps, 2002.
5 Capogna L. Regularity o f quas-i linear equations in the Heisenberg gr oup[ J] . Comm Pur e and Appl Math, 1997, L: 867~ 889.

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Last Update: 2013-03-17