{"paper":{"title":"Monotonicity of principal eigenvalue for elliptic operators with incompressible flow: A functional approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shuang Liu, Yuan Lou","submitted_at":"2017-09-17T03:33:40Z","abstract_excerpt":"We establish the monotonicity of the principal eigenvalue $\\lambda_1(A)$, as a function of the advection amplitude $A$, for the elliptic operator $L_{A}=-\\mathrm{div}(a(x)\\nabla)+A\\mathbf{V}\\cdot\\nabla +c(x)$ with incompressible flow $\\mathbf{V}$, subject to Dirichlet, Robin and Neumann boundary conditions. As a consequence, the limit of $\\lambda_1(A)$ as $A\\to \\infty$ always exists and is finite for Robin boundary conditions. These results answer some open questions raised by [Berestycki, H., Hamel, F., Nadirashvili, N.: Elliptic eigenvalue problems with large drift and applications to nonlin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05606","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":""},"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"}