{"paper":{"title":"Group invariant solutions of certain partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Friedrich Tomi, Jaime Ripoll","submitted_at":"2020-07-02T11:56:52Z","abstract_excerpt":"Let $M$ be a complete Riemannian manifold and $G$ a Lie subgroup of the isometry group of $M$ acting freely and properly on $M.$ We study the Dirichlet Problem \\begin{align*} \\operatorname{div}\\left( \\frac{a\\left( \\left\\Vert \\nabla u\\right\\Vert \\right) }{\\left\\Vert \\nabla u\\right\\Vert }\\nabla u\\right) & =0\\text{ in }\\Omega\\\\ u|\\partial\\Omega & =\\varphi \\end{align*} where $\\Omega$ is a $G-$invariant domain of $C^{2,\\alpha}$ class in $M$ and $\\varphi\\in C^{0}\\left( \\partial\\overline{\\Omega}\\right) $ a $G-$invariant function. Two classical PDE's are included in this family: the $p-$Laplacian $(a("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.01040","kind":"arxiv","version":2},"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/2007.01040/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"}