Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 5, p. 925-963
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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 φ z+ t[φ 2 /2]=w, where w is a bounded measurable function.
DOI : https://doi.org/10.1016/j.anihpc.2014.05.001
Keywords: Intrinsic Lipschitz graphs, Heisenberg groups, Lagrangian formulation, Scalar balance laws, Continuous solutions, Peano phenomenon
@article{AIHPC_2015__32_5_925_0,
     author = {Bigolin, F. and Caravenna, L. and Serra Cassano, F.},
     title = {Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {5},
     year = {2015},
     pages = {925-963},
     doi = {10.1016/j.anihpc.2014.05.001},
     zbl = {1331.35089},
     mrnumber = {3400438},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_5_925_0}
}
Bigolin, F.; Caravenna, L.; Serra Cassano, F. Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 5, pp. 925-963. doi : 10.1016/j.anihpc.2014.05.001. http://www.numdam.org/item/AIHPC_2015__32_5_925_0/

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