A weak comparison principle in tubular neighbourhoods of embedded manifolds

TL;DR

This paper investigates the validity of the weak comparison principle for degenerate quasilinear elliptic equations with first order terms in unbounded tubular domains, showing it holds under certain conditions when the domain is sufficiently narrow.

Contribution

It establishes a weak comparison principle in tubular neighborhoods of embedded manifolds for a class of degenerate elliptic equations, under specific geometric constraints.

Findings

Weak comparison principle holds in narrow tubular domains.

The principle applies to degenerate quasilinear elliptic equations with first order terms.

Results depend on the domain's width and geometric properties.

Abstract

We study weak solutions to degenerate quasilinear elliptic equations, involving first order terms, in unbounded tubular domains. In particular we show that, under suitable hypotheses, the weak comparison principle holds if the domain is narrow enough.