{"paper":{"title":"Brezis-Nirenberg type result for Kohn Laplacian with critical Choquard Nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Divya Goel, K. Sreenadh","submitted_at":"2019-06-25T16:16:42Z","abstract_excerpt":"In this article, we are study the following Dirichlet problem with Choquard type non linearity \\[ -\\Delta_{\\mathbb{H}} u = a u+ \\left(\\int_{\\Omega}\\frac{|u(\\eta)|^{Q^*_\\lambda}}{|\\eta^{-1}\\xi|^{\\lambda}}d\\eta\\right)|u|^{Q^*_\\lambda-2}u \\; \\text{in}\\; \\Omega,\\quad\n  u = 0 \\; \\text{ on } \\partial \\Omega , \\]\n  where $\\Omega$ is a smooth bounded subset of the Heisenberg group $\\mathbb{H}^N, N\\in \\mathbb N$ with $C^2$ boundary and $\\Delta_{\\mathbb{H}}$ is the Kohn Laplacian on the Heisenberg group $\\mathbb{H}^N$. Here, $Q^*_\\lambda=\\frac{2Q-\\lambda}{Q-2},\\; Q= 2N+2$ and $a$ is a positive real para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10628","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"}