Differential equations with non-standard growth have been a very active field of investigation
in recent years. In this survey we present an overview of the field, as well as several of the …

Extending the well-known connection between classical linear potential theory and
probability theory (through the interplay between harmonic functions and martingales) to the …

This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited
many features from the ordinary Laplace Equation, and is based on lectures by the author …

Γ-convergence results for power-law functionals with variable exponents are obtained. The
main motivation comes from the study of (first-failure) dielectric breakdown. Some …

Harnack's inequality and the strong p(⋅)-Laplacian Page 1 J. Differential Equations 250 (2011)
1631–1649 Contents lists available at ScienceDirect Journal of Differential Equations www.elsevier.com/locate/jde …

We consider the following problem: given a bounded domain Ω⊂ Rn and a vector field ζ:
Ω→ Rn, find a solution to− Δ∞ u−〈 Du, ζ〉= 0 in Ω, u= f on∂ Ω, where Δ∞ is the 1 …

Quasiregular mappings with distortion K and solutions of the p-Laplace equation have both
been recently extended to the case where the parameter K or p is a function depending on …

In this note we study the limit as p (x)→∞ of solutions to− Δp (x) u= 0 in a domain Ω, with
Dirichlet boundary conditions. Our approach consists in considering sequences of variable …

The asymptotic behavior of the sequence {un} of positive first eigenfunctions for a class of
inhomogeneous eigenvalue problems is studied in the setting of Orlicz-Sobolev spaces …

In this paper we study the behaviour of the solutions to the eigenvalue problem
corresponding to the p (x)-Laplacian operator as p (x)→∞. We consider a sequence of …