{"title":"Parabolic Systems with measurable coefficients in weighted Sobolev spaces","authors":"Doyoon Kim, Kyeong-Hun Kim, Kijung Lee","doi":"10.3934/cpaa.2022062","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>We present a weighted <inline-formula><tex-math id=\"M1\">\\begin{document}$ L_p $\\end{document}</tex-math></inline-formula>-theory of parabolic systems on a half space <inline-formula><tex-math id=\"M2\">\\begin{document}$ {\\mathbb{R}}^d_+ $\\end{document}</tex-math></inline-formula>. The leading coefficients are assumed to be only measurable in time <inline-formula><tex-math id=\"M3\">\\begin{document}$ t $\\end{document}</tex-math></inline-formula> and have small bounded mean oscillations (BMO) with respect to the spatial variables <inline-formula><tex-math id=\"M4\">\\begin{document}$ x $\\end{document}</tex-math></inline-formula>, and the lower order coefficients are allowed to blow up near the boundary.</p>","PeriodicalId":435074,"journal":{"name":"Communications on Pure & Applied Analysis","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure & Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/cpaa.2022062","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We present a weighted \begin{document}$ L_p $\end{document}-theory of parabolic systems on a half space \begin{document}$ {\mathbb{R}}^d_+ $\end{document}. The leading coefficients are assumed to be only measurable in time \begin{document}$ t $\end{document} and have small bounded mean oscillations (BMO) with respect to the spatial variables \begin{document}$ x $\end{document}, and the lower order coefficients are allowed to blow up near the boundary.
We present a weighted \begin{document}$ L_p $\end{document}-theory of parabolic systems on a half space \begin{document}$ {\mathbb{R}}^d_+ $\end{document}. The leading coefficients are assumed to be only measurable in time \begin{document}$ t $\end{document} and have small bounded mean oscillations (BMO) with respect to the spatial variables \begin{document}$ x $\end{document}, and the lower order coefficients are allowed to blow up near the boundary.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
