On the construction of difference schemes for a second order elliptic differential equation

1966 ◽  
Vol 6 (3) ◽  
pp. 139-151 ◽  
Author(s):  
V.V. Badagadze
Keyword(s):  
Differential Equation ◽  
Second Order ◽  
Difference Schemes ◽  
Elliptic Differential Equation

scholarly journals Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

scholarly journals On non-elliptic boundary problems

1982 ◽  
Vol 86 ◽  
pp. 1-38
Author(s):  
Yoshio Kato
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Boundary Problems

The purpose of this paper is to study the boundary value problems for the second order elliptic differential equation

scholarly journals On a class of non-elliptic boundary problems

1974 ◽  
Vol 54 ◽  
pp. 7-20 ◽  
Author(s):  
Yoshio Kato
Keyword(s):  
Differential Equation ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Boundary Problems

Let Ω be a bounded domain in Rl (l ≥ 2) with, C∞ boundary Γ of dimension l — 1 and let there be given a second order elliptic differential equation(1) in Ω,where ∂j = ∂/∂xi and all coefficients are assumed, for the sake of simplicity, to be real-valued and C∞ on .

scholarly journals Integral operator and oscillation of second order elliptic equations

2005 ◽  
Vol 36 (2) ◽  
pp. 93-101 ◽  
Author(s):  
Zhiting Xu ◽  
Hongyan Xing
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Elliptic Equations ◽  
Second Order ◽  
Elliptic Differential Equation ◽  
Oscillation Criteria ◽  
Second Order Elliptic Equations

By using integral operator, some oscillation criteria for second order elliptic differential equation$$ \sum^d _{i,j=1} D_i[A_{ij}(x)D_jy]+ q(x)f(y)=0, \;x \in \Omega\qquad \eqno{(E)} $$are established. The results obtained here can be regarded as the extension of the well-known Kamenev theorem to Eq.$(E)$.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

Sign in / Sign up

Export Citation Format

Share Document