{"paper":{"title":"Differential games and Hamilton-Jacobi equations in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Calogero","submitted_at":"2018-03-01T17:50:43Z","abstract_excerpt":"The purpose of this work is twofold. First we study the solutions of a Hamilton-Jacobi equation of the form $u_t(t,x)+\\mathcal{H}(t,x,\\nabla_H u(t,x))=0$, where $\\nabla_H u$ represents the horizontal gradient of a function $u$ defined on the Heisenberg group ${I\\!\\!H}$. Motivated by the recent paper by Liu, Manfredi and Zhou (\\cite{LiMaZh2016}), we prove a Lipschitz continuity preserving property for $u$ with respect to the Kor\\'anyi homogeneous distances $d_G$ in ${I\\!\\!H}$. Secondly, we are keenly interested in introducing the game theory in ${I\\!\\!H}$, taking into account its Sub-Riemannian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00528","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}