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We obtain this result by deriving global $W^{1,p}$-estimates of Calder\u00f3n--Zygmund type for a class of nonlinear reaction-diffusion equations with self-diffusion. These estimates are achieved by employing the Caffarelli--Peral perturbation technique together with a new two-parameter scaling argument.<\/jats:p>","DOI":"10.1137\/140981447","type":"journal-article","created":{"date-parts":[[2015,6,2]],"date-time":"2015-06-02T12:27:32Z","timestamp":1433248052000},"page":"2122-2177","source":"Crossref","is-referenced-by-count":32,"title":["Gradient Estimates and Global Existence of Smooth Solutions to a Cross-Diffusion System"],"prefix":"10.1137","volume":"47","author":[{"given":"Luan T.","family":"Hoang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Truyen V.","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tuoc V.","family":"Phan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,6,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.57262\/die\/1371586185","volume":"3","author":"Amann H.","year":"1990","journal-title":"Differential Integral Equations"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01215256"},{"key":"atypb3","first-page":"9","author":"Amann H.","year":"1993","journal-title":"Stuttgart"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.08.018"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-007-0278-y"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-005-0357-6"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.2307\/1971480"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/043"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199801)51:1<1::AID-CPA1>3.0.CO;2-G"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2003.9.1193"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2004.10.719"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01162244"},{"key":"atypb13","volume-title":"Universitext","author":"DiBenedetto E.","year":"1993"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.09.076"},{"key":"atypb15","volume-title":"Classics in Math","author":"Gilbarg D.","year":"2001"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(84)90115-9"},{"key":"atypb17","volume-title":"AMS","author":"Ladyzenskaja O. 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