Abstract: In this talk we discuss some Γ-convergence results for power-law functionals with variable exponents. From the point of view of real world applications the main motivation of the results comes from the study of (first-failure) dielectric breakdown. Some connections with the generalization of the ∞-Laplace equation to the variable exponent setting are also explored. This is joint work with Marian Bocea (Loyola University Chicago).