Next, we study the bi-Laplacian and associated equations: the iterated Poisson equation, the bi-Laplace Neumann and Dirichlet problems, and the "plate equation". It turns out that the bi-Laplace Dirichlet to Neumann map is of non-trivial interest. The exposition concludes with two detailed ...
Pierre-Simon 1749–1827 Marquis de Laplace French astronomer and mathematician Dictionary Entries Near Laplace lap joint Laplace Laplace's equation See More Nearby Entries Cite this Entry Style “Laplace.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/...
As the main problem, the bi-Laplace equation, being a model from fracture mechanics/elasticity, $\D^2 u=0 \quad (\D=D_x^2+D_y^2)$ in a bounded domain $\O \subset e^2$, with inhomogeneous Dirichlet or Navier-type conditions on the smooth boundary $\p \O$ is considered. In ...
p-sub-Laplace算子 1. In this paper, we discuss some nonexistences related to p-sub-Laplacian inequalities on the Heisenberg group and p-degenerate sub-elliptic inequalities constructed by generalized Baouendi-Grushin vector fields. 本文研究了Heisenberg群上相应于p-sub-Laplace算子△_(H,p)的不等...
❄️❄️❄️巴赫《哥德堡变奏曲》(朱晓玫)#bilibili# http://t.cn/A6qTgu6m
On any bounded domain the Dirichlet or Neumann–Laplace operator has a first eigenfunction which is the unique one of fixed sign. For the bilaplace operator, as for any fourth order operator, there is no direct maximum principle and hence no obvious argument for a first eigenfunction of one ...
Its proof requires the introduction of an appropriate semi-classical calculus and a delicate microlocal argument.doi:10.1023/A:1012477708874Jérôme Le RousseauLuc RobbianoA spectral inequality for the bi-laplace operator, preprint (2015), 48 pages....
Chen, Particular solution of Laplace and Bi-harmonic operators using Matern radial basis function, Appl. Math. Lett. 46 (2015) 50-56.Lamichhane, AR, Chen CS. Particular solutions of Laplace and bi-harmonic operators using Matern radial basis function. Int J of Compu Math. DOI: 10.1080/...
In addition, we derive an implicit upper bound for the nodal sets of solutions. We show two types of doubling inequalities for the solutions of bi-Laplace equations. As a consequence, the rate of vanishing is given for the solutions.doi:10.1007/s00205-018-01349-2Jiuyi Zhu...
Blow-up scaling and global behaviour of solutions of the bi-Laplace equation in domains via pencil operators 来自 EBSCO 喜欢 0 阅读量: 51 作者: VA Galaktionov,Pablo Álvarez-Caudevilla 摘要: As the main problem, the bi-Laplace equation \\begin{eqnarray} \\Delta^2 u=0 \\quad (\...