Nonexistence of positive singular solutions for a class of semilinear elliptic systems.
Numerical analysis of the general biharmonic problem by the finite element method
The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform -ellipticity are found.
On a potential problem with incident wave as a field source
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On certain p-harmonic functions in the plane.
On existence in the Cauchy problem for the biharmonic equation
On numerical solution of a variational inequality of the 4th order by finite element method
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
On the Convergence of the Conjugate Gradient Method for Singular Capacitance Matrix Equations from the Neumann Problem of the Poisson Equation.
On the integral representation of superbiharmonic functions
We consider a nonnegative superbiharmonic function satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions satisfying the condition in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman...
On the numerical solution of the first biharmonic equation
On univalent solutions of the biharmonic equation.
Postprocessing schemes for some mixed finite elements
Riesz-Martin representation for positive super-polyharmonic functions in a Riemannian manifold.
Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
Superlinear CG convergence for special right-hand sides.
Sur une méthode d'éléments finis mixte pour l'équation biharmonique
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator , on an arbitrary bounded Lipschitz domain in . We establish existence and uniqueness results when the boundary values have first derivatives in , and the normal derivative is in . The resulting solution takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of is shown to be in .
The Method of Lines for Poisson's Equation with Nonlinear or Free Boundary Conditions.
Traduzione in equazioni integrali di un problema analogo al problema biarmonico fondamentale