Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation

被引：22

作者：

Bigolin, F. ^{[1
]}

Caravenna, L. ^{[2
]}

Cassano, F. Serra ^{[1
]}

机构：

[1] Dipartimento Matemat Trento, I-38123 Trento, Italy

[2] Univ Oxford, Math Inst, OxPDE, 24-29 St Giles, Oxford OX1 3LB, England

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2015年 / 32卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Intrinsic Lipschitz graphs; Heisenberg groups; Lagrangian formulation; Scalar balance laws; Continuous solutions; Peano phenomenon; IMPLICIT FUNCTION THEOREM; REGULAR HYPERSURFACES; RECTIFIABILITY; PERIMETER;

D O I：

10.1016/j.anihpc.2014.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a characterization of intrinsic Lipschitz graphs in the sub-Riemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation partial derivative phi/partial derivative z+partial derivative/partial derivative t[phi(2)/2] = w, where w is a bounded measurable function. CD 2014 Elsevier Masson SAS. All rights reserved.

引用

页码：925 / 963

页数：39

共 28 条

[1] Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I [J].