The aim of this paper is to establish an abstract theory based on the so-called fractional-
maximal distribution functions (FMDs). From the basic ideas introduced in [1], we develop …

We prove global W 1, q (Ω, RN)-regularity for minimisers of F (u)=∫ Ω F (x, D u) dx satisfying
u≥ ψ for a given Sobolev obstacle ψ. W 1, q (Ω, RN) regularity is also proven for minimisers …

We construct an efficient approach to deal with the global regularity estimates for a class of
elliptic double-obstacle problems in Lorentz and Orlicz spaces. Moreover, in the setting of …

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We consider a nonhomogeneous elliptic problem with an irregular obstacle involving a
discontinuous nonlinearity over an irregular domain in divergence form of p-Laplacian type …

We prove existence results for the obstacle problem related to the porous medium equation.
For sufficiently regular obstacles, we find continuous solutions whose time derivative …

We introduce the concept of localizable solutions of parabolic obstacle problems of p-
Laplace-type with highly irregular obstacles and provide corresponding existence results …

We prove higher integrability of the spatial gradient of weak solutions to parabolic systems
with φ-growth, where φ= φ (t) is a general Orlicz function. The parabolic systems need be …

We prove an existence result for parabolic minimizers of convex variational functionals with
p-growth and irregular obstacles. In particular, the obstacle might be unbounded …

We establish local Calderón–Zygmund estimates for solutions to certain parabolic problems
with irregular obstacles and nonstandard p (x, t)-growth. More precisely, we will show that …