{"title":"导数的乘法不等式，以及非线性微分方程解的平滑性的先验估计","authors":"V. E. Maiorov","doi":"10.1070/SM1992V073N02ABEH002551","DOIUrl":null,"url":null,"abstract":"Inequalities of the following form are proved: if is an arbitrary function and , then where depends only on . The exponent is a limiting exponent. With the inequalities as a basis, imbedding theorems are constructed for classes of solutions of nonlinear singular differential equations in the space of times differentiable functions.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Multiplicative Inequalities for Derivatives, and a Priori Estimates of Smoothness of Solutions of Nonlinear Differential Equations\",\"authors\":\"V. E. Maiorov\",\"doi\":\"10.1070/SM1992V073N02ABEH002551\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Inequalities of the following form are proved: if is an arbitrary function and , then where depends only on . The exponent is a limiting exponent. With the inequalities as a basis, imbedding theorems are constructed for classes of solutions of nonlinear singular differential equations in the space of times differentiable functions.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V073N02ABEH002551\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V073N02ABEH002551","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Multiplicative Inequalities for Derivatives, and a Priori Estimates of Smoothness of Solutions of Nonlinear Differential Equations
Inequalities of the following form are proved: if is an arbitrary function and , then where depends only on . The exponent is a limiting exponent. With the inequalities as a basis, imbedding theorems are constructed for classes of solutions of nonlinear singular differential equations in the space of times differentiable functions.
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