Estimates for functions in Sobolev spaces defined on unbounded domains

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

Nonexpansive Mappings Defined on Unbounded Domains

In the study of nonexpansive mappings and fixed point theory the domain of the mapping is usually assumed to be bounded or, as in certain approximation results (see, e.g., [20]), fixed points are assumed to exist. However in [21] Penot used uniform asymptotic concepts which he had earlier introduced in [22] to extend the Browder-Göhde-Kirk theorem to unbounded sets. The term “asymptotic” is use...

A Moser-type inequality in Lorentz-Sobolev spaces for unbounded domains in RN

We derive a Trudinger-Moser type embedding for the Lorentz-Sobolev space W 1 0 L (Ω), where Ω ⊆ R is any sufficiently smooth domain and in particular for Ω = R . Precisely, we first prove that the corresponding inequality is domain independent and then, by constructing explicit concentrating sequences à la Moser, we establish that the embedding inequality is sharp.

Hilbert scales and Sobolev spaces defined by associated Legendre functions

In this paper we study the Hilbert scales defined by the associated Legendre functions for arbitrary integer values of the parameter. This problem is equivalent to study the left–definite spectral theory associated to the modified Legendre equation. We give several characterizations of the spaces as weighted Sobolev spaces and prove identities among the spaces corresponding to lower regularity ...

Error estimates on anisotropic ℚ1 elements for functions in weighted Sobolev spaces

In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. ...