Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials

Yomgne, Gael Diebou

doi:10.1016/j.na.2021.112623

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…The American customer satisfaction index model simplifies the complex indicators [ 13 ], combines the contents of similar indicators, defines the role of customers, and realizes dynamic analysis. Compared with other models, the index of the American customer satisfaction index model is more comprehensive, the evaluation process is simpler [ 14 ], and the analysis dimension is reduced, which is suitable for diversified customer satisfaction analysis. However, the American customer satisfaction index model is easy to fall into local extremum, and about 2–8% of the results are local extremum, which affects the accuracy of satisfaction evaluation.…”

Section: Methodsmentioning

confidence: 99%

[Retracted] Analysis and Research on Audience Satisfaction of Performing Arts Projects in Tourist Scenic Spots Based on the ASCI Model and Big Data

Ding

2022

Journal of Environmental and Public Health

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The development trend of tourism performance networking, although convenient for audience consumption, also makes the performance information present the development trend of big data. In the mass of information, how to accurately locate products and improve audience satisfaction is an urgent problem to be solved. In order to better explore the evaluation of tourism performance by the customer satisfaction evaluation model, analyze the development prospect of tourism in Jiangxi Province in the future, improve the customer satisfaction evaluation model with rough set, and propose a composite customer satisfaction evaluation model. By setting the adjustment value of the evaluation index, the model not only avoids the “false eigenvalue” of the satisfaction evaluation result but also simplifies the calculation process of the model and improves the accuracy, calculation efficiency, and single data processing capacity of the satisfaction evaluation. According to the MATLAB simulation results, the composite customer satisfaction evaluation model constructed in this study is better, the calculation accuracy is >97%, and the calculation time is 40 seconds, which are better than the original customer satisfaction evaluation model. Therefore, the composite customer satisfaction evaluation model can be applied to the evaluation of tourism performance products to provide data support for the evaluation price of audience satisfaction in Jiangxi Province.

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Section: Methodsmentioning

confidence: 99%

[Retracted] Analysis and Research on Audience Satisfaction of Performing Arts Projects in Tourist Scenic Spots Based on the ASCI Model and Big Data

Ding

2022

Journal of Environmental and Public Health

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Dirichlet problem for weakly harmonic maps with rough data

Yomgne

Koch

2022

Communications in Partial Differential Equations

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On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space

Yomgne¹

2022

CPAA

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We consider in this paper the nonlinear elliptic equation with Neumann boundary condition<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \begin{cases} \Delta u = a|u|^{m-1}u\, \, \mbox{ in }\, \, \mathbb{R}^{n+1}_{+}\\ \dfrac{\partial u}{\partial t} = b|u|^{\eta-1}u+f\, \, \mbox{ on }\, \, \partial \mathbb{R}^{n+1}_{+}. \end{cases} \end{align*} $\end{document} </tex-math></disp-formula>For <inline-formula><tex-math id="M1">\begin{document}$ a, b\neq 0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ m>\frac{n+1}{n-1} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ (n>1) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ \eta = \frac{m+1}{2} $\end{document}</tex-math></inline-formula> and small data <inline-formula><tex-math id="M5">\begin{document}$ f\in L^{\frac{nq}{n+1}, \infty}(\partial \mathbb{R}^{n+1}_{+}) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ q = \frac{(n+1)(m-1)}{m+1} $\end{document}</tex-math></inline-formula> we prove that the problem is solvable. More precisely, we establish existence, uniqueness and continuous dependence of solutions on the boundary data <inline-formula><tex-math id="M7">\begin{document}$ f $\end{document}</tex-math></inline-formula> in the function space <inline-formula><tex-math id="M8">\begin{document}$ \mathbf{X}^{q}_{\infty} $\end{document}</tex-math></inline-formula> where<disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \|u\|_{ \mathbf{X}^{q}_{\infty}} = \sup\limits_{t>0}t^{\frac{n+1}{q}-1}\|u(t)\|_{L^{\infty}( \mathbb{R}^{n})}+\|u\|_{L^{\frac{q(m+1)}{2}, \infty}( \mathbb{R}^{n+1}_{+})}+\|\nabla u\|_{L^{q, \infty}( \mathbb{R}^{n+1}_{+})}. $\end{document} </tex-math></disp-formula>As a direct consequence, we obtain the local regularity property <inline-formula><tex-math id="M9">\begin{document}$ C^{1, \nu}_{loc} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ \nu\in (0, 1) $\end{document}</tex-math></inline-formula> of these solutions as well as energy estimates for certain values of <inline-formula><tex-math id="M11">\begin{document}$ m $\end{document}</tex-math></inline-formula>. Boundary values decaying faster than <inline-formula><tex-math id="M12">\begin{document}$ |x|^{-(m+1)/(m-1)} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M13">\begin{document}$ x\in \mathbb{R}^{n}\setminus\{0\} $\end{document}</tex-math></inline-formula> yield solvability and this decay property is shown to be sharp for positive nonlinearities.Moreover, we are able to show that solutions inherit qualitative features of the boundary data such as positivity, rotational symmetry with respect to the <inline-formula><tex-math id="M14">\begin{document}$ (n+1) $\end{document}</tex-math></inline-formula>-axis, radial monotonicity in the tangential variable and homogeneity. When <inline-formula><tex-math id="M15">\begin{document}$ a, b>0 $\end{document}</tex-math></inline-formula>, the critical exponent <inline-formula><tex-math id="M16">\begin{document}$ m_c $\end{document}</tex-math></inline-formula> for the existence of positive solutions is identified, <inline-formula><tex-math id="M17">\begin{document}$ m_c = (n+1)/(n-1) $\end{document}</tex-math></inline-formula>.

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Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials

Cited by 3 publications

References 19 publications

[Retracted] Analysis and Research on Audience Satisfaction of Performing Arts Projects in Tourist Scenic Spots Based on the ASCI Model and Big Data

[Retracted] Analysis and Research on Audience Satisfaction of Performing Arts Projects in Tourist Scenic Spots Based on the ASCI Model and Big Data

Dirichlet problem for weakly harmonic maps with rough data

On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space

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