In this work, we prove a fixed-point theorem in the variable exponent spaces ℓp(.), when p−=1 without further conditions. This result is new and adds more information regarding modular structure of these spaces. To be precise, our concerns ρ-nonexpansive mappings defined on convex subsets ℓp(.) that satisfy specific condition which call “condition uniform decrease”.

In this article a new method for moving from local to global results in variable exponent function spaces is presented. Several applications of the method are also given: Sobolev and trace embeddings; variable Riesz potential estimates; and maximal function inequalities in Morrey spaces are derived for unbounded domains.

In this article, we extend the well-known concentration compactness principle by Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)-Laplacian with critical growth.

We analyze the asymptotic performance of ensembles of random binning Slepian-Wolf codes, where each type class of the source might have a different coding rate. In particular, we first provide the exact encoder excess rate exponent as well as the decoder error exponent. Then, using the error exponent expression, we determine the optimal rate function, namely, the minimal rate for each type clas...

Abstract. We study the boundary value problem −div((|∇u|1 + |∇u|2)∇u) = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R . We focus on the cases when f±(x, u) = ±(−λ|u| u+ |u|u), where m(x) := max{p1(x), p2(x)} < q(x) < N ·m(x) N−m(x) for any x ∈ Ω. In the first case we show the existence of infinitely many weak solutions for any λ > 0. In the second case we prove that if λ is...

Abstract. We study a functional with variable exponent, 1 ≤ p(x) ≤ 2, which provides a model for image denoising, enhancement, and restoration. The diffusion resulting from the proposed model is a combination of total variation (TV)-based regularization and Gaussian smoothing. The existence, uniqueness, and long-time behavior of the proposed model are established. Experimental results illustrat...

In this paper we extend the well-known concentration – compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)−Laplacian with critical growth.

The effects of uncertainties in the gas-surface interaction and intermolecular interaction models on the hypersonic boundary layer development are investigated using the non-intrusive generalized polynomial chaos method. In particular, uncertainties in the surface shear stress, normal stress, heat flux, flowfield temperature and density resulting from uncertain viscosity exponent, surface tempe...

In this paper, we discuss a class of quasilinear evolution variational inequalities with variable exponent growth conditions in a generalized Sobolev space. We obtain the existence of weak solutions by means of penalty method. Moreover, we study the extinction properties of weak solutions to parabolic inequalities and provide a sufficient condition that makes the weak solutions vanish in a fini...