Open AccessOn the class of caustics by reflection of planar curves
Author(s) -
Alfrederic Josse,
Françoise Pène
Publication year - 2015
Publication title -
annali della scuola normale superiore di pisa. classe di scienze
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.444
H-Index - 37
eISSN - 2036-2145
pISSN - 0391-173X
DOI - 10.2422/2036-2145.201304_003
Subject(s) - algebraic curve , caustic (mathematics) , reflection (computer programming) , intersection (aeronautics) , mathematics , envelope (radar) , gravitational singularity , family of curves , class (philosophy) , geometry , lemma (botany) , closure (psychology) , pure mathematics , mathematical analysis , computer science , law , artificial intelligence , telecommunications , radar , ecology , poaceae , political science , engineering , biology , aerospace engineering , programming language
We consider the area functional for t-graphs in the sub-Riemannian Heisenberg group and study minimizers of the associated Dirichlet problem. We prove that, under a bounded slope condition on the boundary datum, there exists a unique minimizer and that this minimizer is Lipschitz continuous. We also provide an example showing that, in the first Heisenberg group, Lipschitz regularity is sharp even under the bounded slope condition