We study robust regularity estimates for local minimizers of nonlocal functionals with non-
standard growth of (p, q)-type and for weak solutions to a related class of nonlocal …

Local Hölder continuity for fractional nonlocal equations with general growth | Mathematische
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We prove a full Harnack inequality for local minimizers, as well as weak solutions to
nonlocal problems with non-standard growth. The main auxiliary results are local …

Under certain restrictions on s, p, q, the Triebel-Lizorkin spaces can be viewed as
generalised fractional Sobolev spaces W qs, p. In this article, we show that the Bourgain …

The application of fractional calculus-based mathematical models in physics is a well-
established practice. However, a challenge arises due to the variety of fractional operators …

This paper deals with new continuous and compact embedding theorems for the fractional
Musielak-Sobolev spaces in R d. As an application, using the variational methods, we obtain …

Abstract In [13], Brezis–Van Schaftingen–Yung discovered new expression of the Sobolev
semi-norm by replacing the L p (R 2 N) norm in the Gagliardo W s, p (RN) semi-norm with …

We consider a non-local Shrödinger problem driven by the fractional Orlicz g-Laplace
operator as follows (P)(−△ g) α u+ g (u)= K (x) f (x, u), in R d, where d≥ 3,(−△ g) α is the …

We consider weak solutions (u, π): Ω→ ℝ n× ℝ to stationary ϕ-Navier-Stokes systems of the
type− div a (x, E u)+∇ π+[D u] u= f div u= 0 in Ω⊂ ℝ n, and to the corresponding ϕ-Stokes …

In this paper, we study a nonlocal generalized Kirchhoff problem driven by the fractional
Orlicz g-Laplace operator and involving a nonsmooth nonlinearity. Although this problem …