{"paper":{"title":"On the asymptotic Dirichlet problem for a class of mean curvature type partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jaime Bruck Ripoll, Jean-Baptiste Casteras, Leonardo Prange Bonorino, Miriam Telichevesky, Patricia Kruse Klaser","submitted_at":"2018-11-24T17:43:42Z","abstract_excerpt":"We study the Dirichlet problem for the following prescribed mean curvature PDE $$ \\begin{cases} -\\operatorname{div}\\dfrac{\\nabla v}{\\sqrt{1+|\\nabla v|^{2}}}=f(x,v) \\text{ in }\\Omega\\\\ v=\\varphi \\text{ on }\\partial\\Omega. \\end{cases} $$ where $\\Omega$ is a domain contained in a complete Riemannian manifold $M,$ $f:\\Omega\\times\\mathbb{R\\rightarrow R}$ is a fixed function and $\\varphi$ is a given continuous function on $\\partial\\Omega$. This is done in three parts. In the first one we consider this problem in the most general form, proving the existence of solutions when $\\Omega$ is a bounded $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09867","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.09867/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}