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- W3137620248 abstract "<p style='text-indent:20px;'>In this paper, we focus on the regularity of nonnegative solutions of Lane-Emden system <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{equation*} begin{cases} -Delta u = v^p -Delta v = u^q end{cases} mbox{ in } mathbb{R}^n. end{equation*} $end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>By means of Kelvin transform, we turn this problem into estimating the local integrability of <inline-formula><tex-math id=M1>begin{document}$ (bar{u},bar{v}) $end{document}</tex-math></inline-formula>. Assume that <inline-formula><tex-math id=M2>begin{document}$ (bar{u},bar{v}) $end{document}</tex-math></inline-formula> possesses some initial local integrability beforehand. <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE2> begin{document}$ (bar{u},bar{v})in L_{loc}^{r_0}(mathbb{R}^n)times L_{loc}^{s_0}(mathbb{R}^n) $end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>for any suitable <inline-formula><tex-math id=M3>begin{document}$ r_0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M4>begin{document}$ s_0 $end{document}</tex-math></inline-formula> under specified conditions. Then through a regularity lifting method by contracting operators, we prove that <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE3> begin{document}$ (bar{u},bar{v})in L_{loc}^r(mathbb{R}^n)times L_{loc}^s(mathbb{R}^n) $end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>for <inline-formula><tex-math id=M5>begin{document}$ r $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M6>begin{document}$ s $end{document}</tex-math></inline-formula> sufficiently large under twice regularity lifting if needed. Furthermore, we lift the regularity of solutions to <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE4> begin{document}$ L^infty(mathbb{R}^n)times L^infty(mathbb{R}^n). $end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>We believe that these new methods employed in this paper can be widely applied to study a variety of other problems with different spaces and linear or nonlinear problems." @default.
- W3137620248 created "2021-03-29" @default.
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- W3137620248 date "2021-01-01" @default.
- W3137620248 modified "2023-09-25" @default.
- W3137620248 title "The regularity lifting methods for nonnegative solutions of Lane-Emden system" @default.
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- W3137620248 doi "https://doi.org/10.3934/cpaa.2021036" @default.
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