An L∞ Bound for the Neumann Problem of the Poisson Equations
نویسندگان
چکیده
In this paper we establish an L∞-bound for the Neumann problem of the Poisson equations. We first develop some estimates for the bounds of solutions in several spaces using Poincarés inequality, Trace theorem and Sobolev’s embedding theorem, and then prove our main theorem utilizing the De Giorgi-Nash estimates.
منابع مشابه
A Boundary Meshless Method for Neumann Problem
Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...
متن کاملAsymptotic distributions of Neumann problem for Sturm-Liouville equation
In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.
متن کاملSemiconductor Device Simulation by a New Method of Solving Poisson, Laplace and Schrodinger Equations (RESEARCH NOTE)
In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as Poisson, Lap lace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in sever...
متن کاملApproximate solution of fourth order differential equation in Neumann problem
Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...
متن کاملAn efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions
In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011