{"paper":{"title":"A Lewy-Stampacchia Estimate for quasilinear variational inequalities in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Pinamonti, Enrico Valdinoci","submitted_at":"2011-05-25T16:09:52Z","abstract_excerpt":"We consider an obstacle problem in the Heisenberg group framework, and we prove that the operator on the obstacle bounds pointwise the operator on the solution. More explicitly, if $\\epsilon\\ge0$ and $\\bar u_\\epsilon$ minimizes the functional $$ \\int_\\Omega(\\epsilon+|\\nabla_{\\H^n}u|^2)^{p/2}$$ among the functions with prescribed Dirichlet boundary condition that stay below a smooth obstacle $\\psi$, then \n0 \\le \\div_{\\H^n}\\, \\Big((\\epsilon+|\\nabla_{\\H^n}\\bar u_\\epsilon|^2)^{(p/2)-1} \\nabla_{\\H^n}\\bar u_\\epsilon\\Big) \n\\qquad \\le (\\div_{\\H^n}\\, \\Big((\\epsilon+|\\nabla_{\\H^n}\\psi|^2)^{(p/2)-1} \\nab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5075","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"}