Lagrange multipliers for higher order elliptic operators

Lagrange Multipliers for Higher Order Elliptic Operators

In this paper, the Babuška’s theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions. Mathematics Subject Classification. 41A10, 41A17, 65N15, 65N30. Received: April 5, 2004.

On the Bethe-Sommerfeld conjecture for higher-order elliptic operators

We consider the elliptic operator P(D)+ V in R , d ≥ 2 where P(D) is a constant coefficient elliptic pseudo-differential operator of order 2 with a homogeneous convex symbol P(ξ), and V is a real periodic function in L∞(Rd). We show that the number of gaps in the spectrum of P(D)+V is finite if 4 > d + 1. If in addition, V is smooth and the convex hypersurface {ξ ∈ R : P(ξ) = 1} has positive Ga...

Efficient Preconditioners Based on Fictitious Domains for Elliptic Fe{problems with Lagrange Multipliers Eecient Preconditioners Based on Ctitious Domains for Elliptic Fe{problems with Lagrange Multipliers

The macro{hybrid formulation based on domain decomposition is considered for elliptic boundary value problems with both symmetric positive deenite and indeenite operators. The problem is discretized by the mortar element method, which leads to a large{scale sparse linear system with a saddle{ point matrix. In the case of symmetric and positive deenite operators, a block diagonal preconditioner ...

Local Hardy Spaces Associated with Inhomogeneous Higher Order Elliptic Operators

Let L be a divergence form inhomogeneous higher order elliptic operator with complex bounded measurable coefficients. In this article, for all p ∈ (0, ∞) and L satisfying a weak ellipticity condition, the authors introduce the local Hardy spaces hpL(R ) associated with L, which coincide with Goldberg’s local Hardy spaces h(R) for all p ∈ (0, ∞) when L ≡ −∆ (the Laplace operator). The authors al...

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS