{"paper":{"title":"Strictly hyperbolic Cauchy problems with coefficients low-regular in time and space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Lorenz","submitted_at":"2018-07-16T12:03:18Z","abstract_excerpt":"We consider the strictly hyperbolic Cauchy problem\n  \\begin{align*}\n  &D_t^m u - \\sum\\limits_{j = 0}^{m-1} \\sum\\limits_{|\\gamma|+j = m} a_{m-j,\\,\\gamma}(t,\\,x) D_x^\\gamma D_t^j u = 0, \\newline\n  &D_t^{k-1}u(0,\\,x) = g_k(x),\\,k = 1,\\,\\ldots,\\,m,\n  \\end{align*}\n  for $(t,\\,x) \\in [0,\\,T]\\times \\mathbb{R}^n$ with coefficients belonging to the Zygmund class $C^s_\\ast$ in $x$ and having a modulus of continuity below Lipschitz in $t$. Imposing additional conditions to control oscillations, we obtain a global (on $[0,\\,T]$) $L^2$ energy estimate without loss of derivatives for $s \\geq \\{1+\\varepsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05811","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"}