{"paper":{"title":"$L^p$-$L^q$ estimates for Electromagnetic Helmholtz equation. Singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andoni Garc\\'ia","submitted_at":"2013-10-09T12:53:26Z","abstract_excerpt":"In space dimension $n\\geq3$, we consider the electromagnetic Schr\\\"odinger Hamiltonian $H=(\\nabla-iA(x))^2+V$ and the corresponding Helmholtz equation\n  (\\nabla-iA(x))^2u+u+V(x)u=f\\quad \\text{in}\\quad \\mathbb{R}^n, where the magnetic and electric potentials are allowed to have singularities at the origin and decay at infinity. We extend the well known $L^p$-$L^q$ estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian $H$ is considered. This work extends the results that appear in \\cite{G}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2457","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"}