Singular perturbation problems for linear elliptic differential operators of arbitrary order. I. Degeneration to elliptic operators

Boundary value problems for elliptic operators with singular drift terms

Let Ω be a Lipschitz domain in R, n ≥ 3, and L = divA∇ − B∇ be a second order elliptic operator in divergence form with real coefficients such that A is a bounded elliptic matrix and the vector field B ∈ Lloc(Ω) is divergence free and satisfies the growth condition dist(X, ∂Ω)|B(X)| ≤ ε1 for ε1 small in a neighbourhood of ∂Ω. For these elliptic operators we will study on the basis of the theory...

Generalized Picone and Riccati Inequalities for Half-linear Differential Operators with Arbitrary Elliptic Matrices

In the article, we extend the well-known Picone identity for halflinear partial differential equations to equations with anisotropic p-Laplacian.

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type

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.

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS