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 ...
本文研究了Heisenberg群上相应于p-sub-Laplace算子△_(H,p)的不等方程和由广义Baouendi-Grushin向量场构成的退化椭圆L_(p,α)不等方程非平凡弱解的不存在性。4) p-Laplacian operator p-Laplace算子 1. By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and...
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 \\begin{eqnarray} \\Delta^2 u=0 \\quad (\\Delta=D_x^2+D_y^2) \\end{eqnarray} in a bounded domain $\\Omega \\subset R^2$, with inhomogeneous Dirichlet or Navier-type conditions on the smooth boundary $\\partial \\Omega$ is consider...
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 ...
❄️❄️❄️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....
bi-Laplace operatorCarleman estimatethree-ball inequalityunique continuationIn this paper, we prove a three-ball inequality for y satisfying an equation of the formFu, XiaoyuLiao, ZhonghuaSichuan Univ Sch Math Chengdu 610064 Peoples R ChinaMathematical Methods in the Applied Sciences...
Evolution p-bi-Laplace equationmixed finite element methodinf-sup condition and mixed formulationexistence and uniquenessThis article discusses a mixed finite element method combined with the backward-Euler method to study the hyperbolic p-bi-Laplace equation, where the existence and uniqueness of ...