{"paper":{"title":"Weak KAM theory for general Hamilton-Jacobi equations II: the fundamental solution under Lipschitz conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"math.AP","authors_text":"Jun Yan, Lin Wang","submitted_at":"2014-08-17T03:45:07Z","abstract_excerpt":"We consider the following evolutionary Hamilton-Jacobi equation with initial condition: \\begin{equation*} \\begin{cases} \\partial_tu(x,t)+H(x,u(x,t),\\partial_xu(x,t))=0,\\\\ u(x,0)=\\phi(x), \\end{cases} \\end{equation*} where $\\phi(x)\\in C(M,\\mathbb{R})$. Under some assumptions on the convexity of $H(x,u,p)$ with respect to $p$ and the uniform Lipschitz of $H(x,u,p)$ with respect to $u$, we establish a variational principle and provide an intrinsic relation between viscosity solutions and certain minimal characteristics. By introducing an implicitly defined {\\it fundamental solution}, we obtain a v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3791","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"}