A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains
A global second-order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains
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DOI：
10.1007/s00526-023-02538-y
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发表时间：
2022-07
影响因子：
2.1
通讯作者：
Qianyun Miao;Fa Peng;Yuan Zhou
中科院分区：
文献类型：
--
作者：
Qianyun Miao;Fa Peng;Yuan Zhou
Letbe a bounded convex domain with. Suppose thatAis uniformly elliptic and belongs towhenorfor somewhen. For, we establish a global second-order regularity estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\Vert D[|Du|^{p-2} Du]\Vert _{L^2(\Omega )}+\Vert D[ \langle ADu,Du\rangle ^{\frac{p-2}{2} }A Du]\Vert _{L^2(\Omega )} \le C \Vert f\Vert _{L^2(\Omega )} \end{aligned}$$\end{document}for the inhomogeneousp-Laplace type equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\textrm{div}\big (\langle A Du,Du\rangle ^{\frac{p-2}{2}} A Du\big )=f \end{aligned}$$\end{document}inwith Dirichlet or Neumann homogeneous boundary condition. Similar result was also established for certain bounded Lipschitz domains whose boundary is weakly second-order differentiable and satisfies some smallness assumptions.
Letbe a bounded convex domain with. Suppose thatAis uniformly elliptic and belongs towhenorfor somewhen. For, we establish a global second-order regularity estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}\Vert D[|Du|^{p-2} Du]\Vert _{L^2(\Omega )}+\Vert D[ \langle ADu,Du\rangle ^{\frac{p-2}{2} }A Du]\Vert _{L^2(\Omega )} \le C \Vert f\Vert _{L^2(\Omega )} \end{aligned}$$\end{document}for the inhomogeneousp-Laplace type equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\textrm{div}\big (\langle A Du,Du\rangle ^{\frac{p-2}{2}} A Du\big )=f \end{aligned}$$\end{document}inwith Dirichlet or Neumann homogeneous boundary condition. Similar result was also established for certain bounded Lipschitz domains whose boundary is weakly second-order differentiable and satisfies some smallness assumptions.