{"paper":{"title":"Regularity in the two-phase free boundary problems under non-standard growth conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Zheng","submitted_at":"2018-09-23T03:01:38Z","abstract_excerpt":"In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\\mathcal {J}_{\\gamma}(u)=\\int_{\\Omega}\\big(f(x,\\nabla u)+\\lambda_{+} (u^{+})^{\\gamma}+\\lambda_{-}(u^{-})^{\\gamma}+gu\\big)\\text{d}x\\rightarrow \\text{min}$ under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with $\\gamma=0$, chemical reaction problems with $0<\\gamma<1$, and obstacle type problems with $\\gamma=1$. Our results hold not only in the degenerate case of $p> 2$ for $p-$Laplace equations, but also in the sin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08519","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"}