VARIATIONAL BOUNDARY VALUE PROBLEMS FOR QUASI-LINEAR ELLIPTIC EQUATIONS OF ARBITRARY ORDER

Quasi-linear elliptic boundary value problems

The variational iteration method for a class of tenth-order boundary value differential equations

Boundary Value Problems for Elliptic Equations

where án, denotes differentiation in the direction of tlie normal to 8B . As is well known, there are explicit formulas for the solutions of the aboye problems, and one can then give a very careful analysis of the solutions when, say f E LP(áB, do), 1 < p < oo . In both cases, the boundary values are taken in the sense of non-tangential convergence, Le ., if Q E aB, and F(Q) _ F. (Q) _ {X E B1 ...

B-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems

In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.

Chapter 1 Foundations of Elliptic Boundary Value Problems 1 . 1 Euler equations of variational problems

A membrane is a surfacic, in its ground state plane, elastic body, whose potential energy is directly proportional to the change of the surface area. Thus, the ground state can be described by a bounded domain Ω ⊂ lR with boundary Γ = ∂Ω which we assume to be piecewise smooth. Under the influence of a force with density f = f(x), x ∈ Ω, which acts perpendicular to the (x1, x2)-plane, the membra...