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On Elliptic Partial Differential Equations [PDF]

, 2011
This series of lectures will touch on a number of topics in the theory of elliptic differential equations. In Lecture I we discuss the fundamental solution for equations with constant coefficients. Lecture 2 is concerned with Calculus inequalities including the well known ones of Sobolev. In lectures 3 and 4 we present the Hilbert space approach to the
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Applications to Elliptic Partial Differential Equations [PDF]

, 2012
We consider elliptic partial differential equations in d variables and their discretisation in a product grid \(\mathbf{I} = \times^{d}_{j=1}I_{j}\). The solution of the discrete system is a grid function, which can directly be viewed as a tensor in \(\mathbf{V} = {\bigotimes}^{d}_{j=1}\mathbb{K}^{I_{j}}\). In Sect.
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Elliptic partial differential equation and optimal control

Numerical Methods for Partial Differential Equations, 1992
AbstractThe theory of optimal control and the semianalytical method of elliptic partial differential equation (PDE) in a prismatic domain are mutually simulated issues. The simulation of discrete‐time linear quadratic (LQ) control with the substructural chain problem in static structural analysis is given first.
Zhong Xiang-Xiang, Zhong Wan-xie
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On solving elliptic stochastic partial differential equations

Computer Methods in Applied Mechanics and Engineering, 2002
The paper solves elliptic boundary value problems of second-order with stochastic coefficients by using a Karhunen-Loève expansion. Estimates in the setup of Sobolev spaces are given. The paper also analyses the method of successive approximations and the perturbation method.
Panagiotis Chatzipantelidis, Ivo Babuška   +1 more
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Partial differential equations I — elliptic equations [PDF]

, 1986
In this chapter we start to examine some techniques used for the numerical solution of partial differential equations (PDEs) and, in particular, equations which are special cases of the linear second-order equation with two independent variables $$a\frac{{{\partial ^2}u}}{{\partial {x^2}}} + b\frac{{{\partial ^2}u}}{{\partial x\partial y}} + c\frac{
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On solvability of a quasi-elliptic partial differential equations

Journal of Elliptic and Parabolic Equations, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nilufer R. Rustamova, Alik M. Najafov, Alik M. Najafov, Sain T. Alekberli   +3 more
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Orthogonal Collocation for Elliptic Partial Differential Equations

SIAM Journal on Numerical Analysis, 1976
An $O(\rho ^4 )$ collocation method ($\rho $ the mesh size) is presented for solving elliptic partial differential equations on the unit square and a convergence proof is given. The method is shown to compare favorably with the Ritz–Galerkin method, and some numerical results demonstrate the effectiveness of the method.
P. M. Prenter, R. D. Russell
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Elliptic Partial Differential Equations

2016
General existence theories for solutions of partial differential equations require using concepts from functional analysis and considering generalizations of classical derivatives based on a multidimensional integration-by-parts formula. The chapter introduces Sobolev spaces, discusses their main properties, states existence theories for elliptic ...
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Partial Differential Equations of Elliptic Type

Physics Bulletin, 1971
C Miranda Berlin: Springer 1970 pp xii + 370 price DM 58 This is a translation of the second revised edition of the monograph published in 1955. The number of pages has risen from 222 to 370 of which 69 are occupied by a bibliography.
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Elliptic Partial Differential Equations

1984
In this chapter we review the main tools used to study elliptic partial differential equations (PDE): Sobolev spaces, variational formulations, and continuous dependence on the data.
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