Generalized Concentration-Compactness Principles for Variable Exponent Lebesgue Spaces with Asymptotic Analysis of Low Energy Extremals

Concentration-compactness Principle for Variable Exponent Spaces and Applications

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.

The Concentration-compactness Principle for Variable Exponent Spaces and Applications

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.

Concentration of low energy extremals: Identification of concentration points

On The Sobolev-type Inequality for Lebesgue Spaces with a Variable Exponent

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces ∗

We prove optimal integrability results for solutions of the p(·)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L to variable exponent weak Lebesgue spaces.