A density result for homogeneous Sobolev spaces

TL;DR

This paper proves that in certain hyperbolic domains, smooth functions with bounded derivatives are dense in the corresponding homogeneous Sobolev spaces, enhancing understanding of function approximation in these spaces.

Contribution

It establishes the density of smooth bounded derivative functions in homogeneous Sobolev spaces within Gromov hyperbolic domains, a new result in geometric analysis.

Findings

Smooth functions with bounded derivatives are dense in $L^{k,p}( abla)$ spaces.

The result applies specifically to bounded Gromov hyperbolic domains.

This advances the theory of function approximation in geometric analysis contexts.

Abstract

We show that in a bounded Gromov hyperbolic domain $\Omega$ smooth functions with bounded derivatives $C^\infty(\Omega)\cap W^{k,\infty}(\Omega)$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega)$.