{"title":"非二重广义Orlicz空间中的Bloch估计","authors":"Petteri Harjulehto, P. Hasto, Jonne Juusti","doi":"10.3934/mine.2023052","DOIUrl":null,"url":null,"abstract":"<abstract><p>We study minimizers of non-autonomous functionals</p>\n\n<p><disp-formula> <label/> <tex-math id=\"FE1\"> \\begin{document}$ \\begin{align*} \\inf\\limits_u \\int_\\Omega \\varphi(x,|\\nabla u|) \\, dx \\end{align*} $\\end{document} </tex-math></disp-formula></p>\n\n<p>when $ \\varphi $ has generalized Orlicz growth. We consider the case where the upper growth rate of $ \\varphi $ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on \"truncating\" the function $ \\varphi $ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.</p></abstract>","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":" ","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Bloch estimates in non-doubling generalized Orlicz spaces\",\"authors\":\"Petteri Harjulehto, P. Hasto, Jonne Juusti\",\"doi\":\"10.3934/mine.2023052\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<abstract><p>We study minimizers of non-autonomous functionals</p>\\n\\n<p><disp-formula> <label/> <tex-math id=\\\"FE1\\\"> \\\\begin{document}$ \\\\begin{align*} \\\\inf\\\\limits_u \\\\int_\\\\Omega \\\\varphi(x,|\\\\nabla u|) \\\\, dx \\\\end{align*} $\\\\end{document} </tex-math></disp-formula></p>\\n\\n<p>when $ \\\\varphi $ has generalized Orlicz growth. We consider the case where the upper growth rate of $ \\\\varphi $ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on \\\"truncating\\\" the function $ \\\\varphi $ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.</p></abstract>\",\"PeriodicalId\":54213,\"journal\":{\"name\":\"Mathematics in Engineering\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.3934/mine.2023052\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mine.2023052","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
when $ \varphi $ has generalized Orlicz growth. We consider the case where the upper growth rate of $ \varphi $ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function $ \varphi $ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.
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