{"paper":{"title":"Radial biharmonic $k-$Hessian equations: The critical dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Escudero, Pedro J. Torres","submitted_at":"2017-06-18T16:35:26Z","abstract_excerpt":"This work is devoted to the study of radial solutions to the elliptic problem \\begin{equation}\\nonumber \\Delta^2 u = (-1)^k S_k[u] + \\lambda f, \\qquad x \\in B_1(0) \\subset \\mathbb{R}^N, \\end{equation} provided either with Dirichlet boundary conditions \\begin{eqnarray}\\nonumber u = \\partial_n u = 0, \\qquad x \\in \\partial B_1(0), \\end{eqnarray} or Navier boundary conditions \\begin{equation}\\nonumber u = \\Delta u = 0, \\qquad x \\in \\partial B_1(0), \\end{equation} where the $k-$Hessian $S_k[u]$ is the $k^{\\mathrm{th}}$ elementary symmetric polynomial of eigenvalues of the Hessian matrix and the dat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05684","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"}