The $ p $-Laplace equation is the main prototype for nonlinear elliptic problems and forms a
basis for various applications, such as injection moulding of plastics, nonlinear elasticity …

Let f: X→ Y be a homeomorphism between locally compact Ahlfors Q-regular metric spaces,
Q> 1. We prove that finiteness of either lipf (x), hf (x), or h∗ f (x) for every x∈ X\E implies that …

In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined
using the notion of (weak) upper gradients, where the summability of a function and its upper …

We prove a Poincaré inequality for Orlicz–Sobolev functions with zero boundary values in
bounded open subsets of a metric measure space. This result generalizes the (p, p) …

Let $ G $ be an Orlicz function and let $\alpha,\beta, s $ be positive real numbers. Under
certain conditions on the Orlicz function $ G $, we establish some continuous embeddings …

In this paper we deal with a metric measure space equipped with a doubling measure and
supporting an Orlicz-Poincaré inequality, namely a weak (1, Φ)-Poincaré inequality, that is …

We introduce a maximal operator for functions defined on a doubling metric measure space,
belonging to a rearrangement Banach function space. We provide some estimates for the …

In the following,(X, d, µ) is a metric measure space, ie a metric space (X, d) endowed with a
Borel regular measure µ, that is finite and positive on balls. We use the definition given by …

In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined
using the notion of (weak) upper gradients, where the summability of a function and its upper …

We introduce a new type of first order Poincaré inequality for functions defined on a metric
measure space, that is an useful tool in the study of Newtonian spaces based on Banach …