Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

Kentaro Hirata

doi:10.1007/s00574-022-00283-y

Hirata, Kentaro

2022-01-15 00:00:00

This paper establishes a removable singularity theorem for the quasilinear elliptic equations with source terms like -Δpu=a|u|q+b|∇u|s+c|u|σ|∇u|τ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\begin{aligned} -\Delta _p u = a |u|^q + b|\nabla u|^s + c|u|^\sigma |\nabla u|^\tau \end{aligned}$$\end{document}with nonnegative bounded Borel measurable functions a, b, c and positive numbers q,s,σ,τ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q,s,\sigma ,\tau $$\end{document}. In particular, we give upper bounds of exponents q,s,σ,τ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q,s,\sigma ,\tau $$\end{document} and a sharp growth condition for nonnegative weak solutions in RN\E\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {R}}^N{\setminus } E$$\end{document} to be extended to the whole of RN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {R}}^N$$\end{document} as solutions, when E is a compact set satisfying a uniform Minkowski condition.

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"Bulletin of the Brazilian Mathematical Society, New Series" Springer Journals

http://www.deepdyve.com/lp/springer-journals/removable-singularities-for-quasilinear-elliptic-equations-with-source-1N07RinnAH

Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

$This paper establishes a removable singularity theorem for the quasilinear elliptic equations with source terms like -Δpu=a|u|q+b|∇u|s+c|u|σ|∇u|τ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\begin{aligned} -\Delta _p u = a |u|^q + b|\nabla u|^s + c|u|^\sigma |\nabla u|^\tau \end{aligned}$$\end{document}with nonnegative bounded Borel measurable functions a, b, c and positive numbers q,s,σ,τ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q,s,\sigma ,\tau $$\end{document}. In particular, we give upper bounds of exponents q,s,σ,τ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q,s,\sigma ,\tau $$\end{document} and a sharp growth condition for nonnegative weak solutions in RN\E\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {R}}^N{\setminus } E$$\end{document} to be extended to the whole of RN\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {R}}^N$$\end{document} as solutions, when E is a compact set satisfying a uniform Minkowski condition.$

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Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

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Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

Removable Singularities for Quasilinear Elliptic Equations with Source Terms Involving the Solution and Its Gradient

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