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Regularity of quasi‐linear equations in the Heisenberg group
Author(s) -
Capogna Luca
Publication year - 1997
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199709)50:9<867::aid-cpa3>3.0.co;2-3
Subject(s) - mathematics , heisenberg group , nilpotent , class (philosophy) , pure mathematics , conformal map , lie group , group (periodic table) , type (biology) , mathematical analysis , quantum mechanics , physics , ecology , artificial intelligence , computer science , biology
We prove the C α regularity of the gradient of weak solutions of a class of quasi‐linear equations in nilpotent stratified Lie groups of step two. As applications, we prove higher regularity theorems and a Liouville type theorem for 1‐quasi‐conformal mappings between domains of the Heisenberg group. © 1997 John Wiley & Sons, Inc.