Approximation by solutions of elliptic equations in semilocal spaces

Approximation in Uniform Norm by Solutions of Elliptic Differential Equations

Introduction. Let G be an open subset of the Euclidean w-space E, Gi an open subset with compact closure in G. If n = 2 and G is the whole of E, an important circle of theorems in the theory of analytic functions associated with the names of Walsh, HartogsRosenthal, Lavrentiev, Keldych, and Mergelyan deals with the possibility of approximating analytic functions on Gi continuous on its closure,...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

GRADED MESH APPROXIMATION IN WEIGHTED SOBOLEV SPACES AND ELLIPTIC EQUATIONS IN 2D By

We study the approximation properties of some general finiteelement spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. The finite-element spaces that we define are obtained from conformally invariant families of finite elements (no affine invariance is used), stressing t...

Elliptic Hypergeometric Solutions to Elliptic Difference Equations⋆

It is shown how to define difference equations on particular lattices {xn}, n ∈ Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.

Sobolev Spaces and Elliptic Equations

Lipschitz domains. Our presentations here will almost exclusively be for bounded Lipschitz domains. Roughly speaking, a domain (a connected open set) Ω ⊂ R is called a Lipschitz domain if its boundary ∂Ω can be locally represented by Lipschitz continuous function; namely for any x ∈ ∂Ω, there exists a neighborhood of x, G ⊂ R, such that G ∩ ∂Ω is the graph of a Lipschitz continuous function und...