{"paper":{"title":"On the velocity averaging for equations with optimal heterogeneous rough coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Darko Mitrovic, Martin Lazar","submitted_at":"2013-10-16T07:33:18Z","abstract_excerpt":"Assume that $(u_n)$ is a sequence of solutions to heterogeneous equations with rough coefficients and fractional derivatives, weakly converging to zero in ${\\rm L}^p(\\R^{d+m})$, with $p>1$.\n  We prove that the sequence of averaged quantities $(\\int \\rho(\\my) u_n(\\mx,\\my) d\\my)$ is strongly precompact in $\\Ljl\\Rd$ for any $\\rho\\in \\Cc{\\R^m}$, provided that restrictive non-degeneracy conditions are satisfied. These are fulfilled for elliptic, parabolic, fractional convection-diffusion equations, as well as for parabolic equations with a fractional time derivative. The main tool that we are using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4285","kind":"arxiv","version":3},"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"}