{"paper":{"title":"H\\\"older bounds and regularity of emerging free boundaries for strongly competing Schr\\\"odinger equations with nontrivial grouping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Zilio, Hugo Tavares, Nicola Soave, Susanna Terracini","submitted_at":"2015-06-02T09:00:52Z","abstract_excerpt":"We study regularity issues for systems of elliptic equations of the type \\[\n  -\\Delta u_i=f_{i,\\beta}(x)-\\beta \\sum_{j\\neq i} a_{ij} u_i |u_i|^{p-1}|u_j|^{p+1} \\] set in domains $\\Omega \\subset \\mathbb{R}^N$, for $N \\geq 1$. The paper is devoted to the derivation of $\\mathcal{C}^{0,\\alpha}$ estimates that are uniform in the competition parameter $\\beta > 0$, as well as to the regularity of the limiting free-boundary problem obtained for $\\beta \\to + \\infty$.\n  The main novelty of the problem under consideration resides in the non-trivial grouping of the densities: in particular, we assume that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00800","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"}