{"paper":{"title":"Bilinear embedding for divergence-form operators with complex coefficients on irregular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Andrea Carbonaro, Oliver Dragi\\v{c}evi\\'c","submitted_at":"2019-05-03T22:39:05Z","abstract_excerpt":"Let $\\Omega\\subseteq \\mathbb{R}^{d}$ be open and $A$ a complex uniformly strictly accretive $d\\times d$ matrix-valued function on $\\Omega$ with $L^{\\infty}$ coefficients. Consider the divergence-form operator ${\\mathscr L}^{A}=-{\\rm div}(A\\nabla)$ with mixed boundary conditions on $\\Omega$. We extend the bilinear inequality that we proved in [16] in the special case when $\\Omega=\\mathbb{R}^{d}$. As a consequence, we obtain that the solution to the parabolic problem $u^{\\prime}(t)+{\\mathscr L}^{A}u(t)=f(t)$, $u(0)=0$, has maximal regularity in $L^{p}(\\Omega)$, for all $p>1$ such that $A$ satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01374","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"}