Higher integrability for nonlinear parabolic equations of plus-plus">p-Laplacian type

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• 作者：Fengping Yao
• 关键词：Higher integrability ; Regularity ; Orlicz ; Nonlinear ; Gradient ; Parabolic ; p ; Laplacian
• 刊名：Archiv der Mathematik
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：108
• 期：1
• 页码：85-97
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-8938
• 卷排序：108

文摘

In this paper we give a new alternative proof of the local higher integrability in Orlicz spaces of the gradient for weak solutions of quasilinear parabolic equations of p-Laplacian type$$\begin{array}{ll} u_t-\text{div} \left( \left | \nabla u\right|^{ p-2 } \nablau\right)=\text{div} \left(| \mathrm{ \bf f}|^{p-2} \mathrm{ \bf f}\right)\quad {\rm in}~\Omega\times (0,T] \end{array}$$for any p > 0. Moreover, we point out that our results are homogeneousregularity estimates in Orlicz spaces and improve the known results for such equations by using some new techniques. Actually, our results can be extended to the global estimates and cover a more general class of degenerate/singular parabolic problems of p-Laplacian type.KeywordsHigher integrabilityRegularityOrliczNonlinearGradientParabolicp-LaplacianMathematics Subject Classification35B4535K55References1.Acerbi E., Mingione G.: Gradient estimates for the p(x)-Laplacean system. J. Reine Angew. 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Anal. 70, 1265–1274 (2009)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsFengping Yao1Email author1.Department of MathematicsShanghai UniversityShanghaiChina About this article CrossMark Publisher Name Springer International Publishing Print ISSN 0003-889X Online ISSN 1420-8938 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; letter-spacing: .017em; 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