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Keyword: Laplacian
Nonresonance between the first two Eigencurves of Laplacian for a Nonautonomous Neumann Problem
We consider the following Neumann elliptic problem \( \left\{ \begin{array}{rl} -\Delta u =\alpha\,m_{1}(x)\,u+m_{2}(x)\,g(u)+h(x)\quad & in \: \Omega,\\ \quad\\ \frac{\partial u}{\partial\nu} = 0\qquad\qquad\qquad\qquad\qquad\qquad\quad& on\: \partial\Omega. \end{array} \right. \) By means of Leray-Schauder degree and under some assumptions on the asymptotic behavior of the potential of the nonlinearity g, we prove an existence result for our equation…
Read More On the Spectrum of problems involving both \(p(x)\)-Laplacian and \(P(x)\)-Biharmonic
We prove the existence of at least one non-decreasing sequence of positive eigenvalues for the problem, $$\begin{gathered}\left\{ \begin{array}{ll} \Delta_{p(x)}^{2}u-\triangle_{p(x)}u= \lambda |u|^{p(x)-2}u, \ \ \quad in \ \Omega \\ u\in W^{2,p(x)}(\Omega)\cap W_{0}^{1,p(x)}(\Omega),\end{array}\right. \end{gathered}$$ Our analysis mainly relies on variational arguments involving Ljusternik-Schnirelmann theory.
Read More 3D Facial Feature Tracking with Multimodal Depth Fusion
As models based in artificial intelligence increase in sophistication, there is a higher demand for the integration of hardware components to heighten real-world implementations. Both facial feature tracking and shape-from-focus are known techniques in computer vision. However, the combination of these two elements, particularly in a cost-effective configuration, has not been extensively explored. In this…
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