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Results tagged with laplacian
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user 48438
The Laplacian matrix is the representation of a graph in matrix form.
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Inequalities concerning principal eigenvalues of Laplacian with different boundary conditions
Suppose $\Omega\subset\mathbb R^2$ is a bounded simply connected domain with sufficiently smooth boundary. Consider the following three BVPs (respectively with Dirchlet, Neumann and certain non-local …
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certain smoothness of principal eigenvalue of Dirichlet Laplacian on polygons
given polygon $P_N$, with side lengths $x_1,\cdots,x_N$ and interior angles $\theta_1,\cdots,\theta_N$ let $\lambda(x_1,\cdots,x_N,\theta_1,\cdots,\theta_N)$ denote the least eigenvalue of Dirichlet Laplacian …
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Universal constant for reverse inequality between first eigenvalues of Neumann and Dirichlet...
bounded simply connected domain with smooth boundary and let $0<\lambda_1^D(\Omega)\leq\lambda_2^D(\Omega)\leq\cdots$ and $0=\lambda_1^N(\Omega)\leq\lambda_2^N(\Omega)\leq\cdots$ denote the eigenvalues of Laplacian …
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A conjecture on shape optimization for Dirichlet-Laplacian
For a given domain $G$, with sufficiently smooth boundary, in the plane we denote the first two eigenvalues of Dirichlet-Laplacian on $G$ of by $\lambda_1(G)$ and $\lambda_2(G)$.
$\textbf{Open(?) …
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