{"title":"Invertibility","authors":"Crista Arangala","doi":"10.1090/mmono/003/06","DOIUrl":"https://doi.org/10.1090/mmono/003/06","url":null,"abstract":". Let Ω, Ω ′ ⊂ R n be bounded domains and let f m : Ω → Ω ′ be a sequence of homeomorphisms with positive Jacobians J f m > 0 a.e. and prescribed Dirichlet boundary data. Let all f m satisfy the Lusin (N) condition and sup m R Ω ( | Df m | n − 1 + A ( | cof Df m | )+ ϕ ( J f )) < ∞ , where A and ϕ are positive convex functions. Let f be a weak limit of f m in W 1 ,n − 1 . Provided certain growth behaviour of A and ϕ , we show that f satisfies the (INV) condition of Conti and De Lellis, the Lusin (N) condition, and polyconvex energies are lower semicontinuous.","PeriodicalId":205141,"journal":{"name":"How to Pass the FRACP Written Examination","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126171048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Abstract Vectors","authors":"","doi":"10.1002/9781119437437.ch5","DOIUrl":"https://doi.org/10.1002/9781119437437.ch5","url":null,"abstract":"","PeriodicalId":205141,"journal":{"name":"How to Pass the FRACP Written Examination","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125670213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Transformations and Matrices","authors":"","doi":"10.1002/9781119437437.ch3","DOIUrl":"https://doi.org/10.1002/9781119437437.ch3","url":null,"abstract":"","PeriodicalId":205141,"journal":{"name":"How to Pass the FRACP Written Examination","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124308964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Index","authors":"","doi":"10.1002/9781119437437.index","DOIUrl":"https://doi.org/10.1002/9781119437437.index","url":null,"abstract":"","PeriodicalId":205141,"journal":{"name":"How to Pass the FRACP Written Examination","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115163828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Matrix Theory","authors":"R. Piziak","doi":"10.1036/1097-8542.410500","DOIUrl":"https://doi.org/10.1036/1097-8542.410500","url":null,"abstract":"","PeriodicalId":205141,"journal":{"name":"How to Pass the FRACP Written Examination","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126623551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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