The trace of u∈Wloc1,1(Ω)⋂L∞(Ω) and its applications View Full Text


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Article Info

DATE

2022-05-02

AUTHORS

Huashui Zhan

ABSTRACT

This paper is concerned with the well-posedness problem of a doubly degenerate parabolic equation with variable exponents. By the parabolically regularized method, the existence of local solution is proved. Moreover, the trace of u∈W01,1(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u\in W^{1,1}_{0}(\Omega )$\end{document} is generalized to u∈Wloc1,1(Ω)⋂L∞(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u\in W^{1,1}_{\mathrm{loc}}(\Omega )\bigcap L^{\infty}(\Omega )$\end{document} in a rational way. Then, a partial boundary value condition matching up with the stability theorem is found. More... »

PAGES

38

References to SciGraph publications

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  • 2021-12-17. Positive solutions of a nonlinear parabolic equation with double variable exponents in ANALYSIS AND MATHEMATICAL PHYSICS
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  • 1973. Second Order Equations With Nonnegative Characteristic Form in NONE
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