This book discusses advances in maximal function methods related to Poincaré and
Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's …

We prove up-to-the-boundary higher integrability estimates for parabolic quasi-minimizers
on a domain Ω T= Ω×(0, T), where Ω denotes an open domain in a doubling metric measure …

This paper studies parabolic quasiminimizers which are solutions to parabolic variational
inequalities. We show that, under a suitable regularity condition on the boundary, parabolic …

The objects of our studies are vector valued parabolic minimizers u associated to a convex
Carathéodory integrand f obeying a p-growth assumption from below and a certain …

We give an existence proof for variational solutions u associated to the total variation flow.
Here, the functions being considered are defined on a metric measure space (X, d, μ) …

We give a new proof for the self-improvement of uniform p-fatness in the setting of general
metric spaces. Our proof is based on rather standard methods of geometric analysis, and in …

We are concerned with the stability property for parabolic quasi minimizers in metric
measure spaces. More precisely we consider a doubling metric measure space X which …

We study local and global higher integrability properties for quasiminimizers of a class of
double phase integrals characterized by nonstandard growth conditions. We work purely on …

The objective of this work is an existence proof for variational solutions u to parabolic
minimizing problems. Here, the functions being considered are defined on a metric measure …

Using purely variational methods, we prove local and global higher integrability results for
upper gradients of quasiminimizers of a (p, q)-Dirichlet integral with fixed boundary data …