Existence and regularity results for a class of non-uniformly elliptic Robin problems

In this paper, we study the existence and the summability of solutions to a Robin boundary value problem whose prototype is the following: [Formula: see text] where [Formula: see text] is a bounded Lipschitz domain in [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] is a positive even function which may vanish at infinity and [Formula: see text] belongs to a suitable Lebesgue space. The presence of such a function [Formula: see text] in the principal part of the operator prevents it from being uniformly elliptic when [Formula: see text] is large.