{"paper":{"title":"A note on the local regularity of distributional solutions and subsolutions of semilinear elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel","submitted_at":"2015-09-05T20:03:09Z","abstract_excerpt":"In this note we prove local regularity results for distributional solutions and subsolutions of semilinear elliptic systems such as $$ L_k^m u_k = f_k(x,u_1,\\ldots,u_N) \\quad\\text{in }\\mathbb{R}^n\\qquad (k=1,\\ldots,N) $$ where $L_1,\\ldots,L_N$ are of divergence-form and $n\\geq 2m$. We show that distributional subsolutions are locally bounded from above if $|f_k(x,z)|\\leq C(1+|z|^p)$ for $1\\leq p<\\frac{n}{n-2m},k=1,\\ldots,N$.\n  Furthermore, regularity properties of subsolutions and improved versions for bounded subsolutions are given. Even for $f_1=\\ldots=f_N=0$ our results are new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01731","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"}