{"paper":{"title":"Nodal Sets for \"Broken\" Quasilinear PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Henrik Shahgholian, Ki-Ahm Lee, Sunghan Kim","submitted_at":"2017-05-31T01:43:37Z","abstract_excerpt":"We study the local behavior of the nodal sets of the solutions to elliptic quasilinear equations with nonlinear conductivity part, \\begin{equation*} \\operatorname{div}(A_s(x,u)\\nabla u)=\\operatorname{div}{\\vec f}(x), \\end{equation*} where $A_s(x,u)$ has \"broken\" derivatives of order $s\\geq 0$, such as \\begin{equation*} A_s(x,u) = a(x) + b(x)(u^+)^s, \\end{equation*} with $(u^+)^0$ being understood as the characteristic function on $\\{u>0\\}$. The vector ${\\vec f}(x)$ is assumed to be $C^\\alpha$ in case $s=0$, and $C^{1,\\alpha}$ (or higher) in case $s>0$.\n  Using geometric methods, we prove almos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10910","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"}