The asymptotic behavior of some power-law functionals in Sobolev spaces with variable exponents

Abstract

In this talk we discuss some $\Gamma$-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 $\infty$-Laplace equation to the variable exponent setting are also explored. This is joint work with Marian Bocea (Loyola University Chicago).