相关论文: Estimates on Pull-in Distances in MEMS Models and …
We examine the regularity of the extremal solution of the nonlinear eigenvalue problem $\Delta^2 u = \lambda f(u)$ on a general bounded domain $\Omega$ in $ \IR^N$, with the Navier boundary condition $ u=\Delta u =0 $ on $ \pOm$. Here $…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a…
A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems.…
We establish a new $W^{1,2\frac{n-1}{n-2}}$ estimate for the extremal solution of $-\Delta u=\lambda f(u)$ in a smooth bounded domain $\Omega$ of $\mathbb{R}^n$, which is convex, for arbitrary positive and increasing nonlinearities $f\in…
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…
In this paper, we are interested in the mathematical model of MEMS devices which is presented by the following equation on $(0,T) \times \Omega:$ \begin{eqnarray*} \partial_t u = \Delta u +\displaystyle \frac{\lambda }{ (1-u)^2 \left( 1…
We consider the problem of finding and describing minimisers of the Rayleigh quotient \[ \Lambda_\infty \, :=\, \inf_{u\in \mathcal{W}^{2,\infty}(\Omega)\setminus\{0\} }\frac{\|\Delta u\|_{L^\infty(\Omega)}}{\|u\|_{L^\infty(\Omega)}}, \]…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
The requirements pertaining to the reliability and accuracy of micro-electromechanical gyroscopic sensors are increasing,as systems for vehicle localization emerge as an enabling factor for autonomous driving. Since micro-electromechanical…
We obtain sharp weighted estimates for solutions of the equation $\partial$ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p ($\Omega$,$\delta$ $\gamma$), $\delta$ being the distance to the…
We consider a second-order nonlocal parabolic MEMS equation with Dirichlet boundary conditions: \[ u_t-\Delta u=\frac{\lambda}{(1-u)^2\bigl(1+\int_\Omega\frac{1}{1-u}\,dx\bigr)^2},\quad x\in\Omega,\ t>0, \] where…
A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at different electrostatic potentials. It couples a second order…
This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems with heterogeneous coefficients. The local approximation…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…
This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to…
This paper studies explicit numerical approximations of the invariant probability measures (IPMs) for stochastic functional differential equations (SFDEs) with infinite delay under one-sided Lipschitz condition on the drift coefficient. To…
We consider least energy solutions to the nonlinear equation $-\Delta_g u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\ge 2$ which include the classical hyperbolic space $\mathbb H^n$ as well as manifolds with…