Γ-convergence of power-law functionals with variable exponents
نویسندگان
چکیده
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 connections with the generalization of the ∞-Laplace equation to the variable exponent setting are also explored. 2000 Mathematics Subject Classification:
منابع مشابه
Power-Law Approximation under Differential Constraints
We study the Γ-convergence of the power-law functionals
متن کاملOn the asymptotic behavior of variable exponent power–law functionals and applications
We study, via -convergence, the asymptotic behavior of several classes of power–law functionals acting on fields belonging to variable exponent Lebesgue spaces and which are subject to constant rank differential constraints. Applications of the -convergence results to the derivation and analysis of several models related to polycrystal plasticity arising as limiting cases of more flexible power...
متن کاملHomogenization in Sobolev Spaces with Nonstandard Growth: Brief Review of Methods and Applications
We review recent results on the homogenization in Sobolev spaces with variable exponents. In particular, we are dealing with the Γ-convergence of variational functionals with rapidly oscillating coefficients, the homogenization of the Dirichlet and Neumann variational problems in strongly perforated domains, as well as double porosity type problems.The growth functions also depend on the small ...
متن کاملModels for growth of heterogeneous sandpiles via Mosco convergence
In this paper we study the asymptotic behavior of several classes of power-law functionals involving variable exponents pn(·) → ∞, via Mosco convergence. In the particular case pn(·) = np(·), we show that the sequence {Hn} of functionals Hn : L(R )→ [0,+∞] given by Hn(u) = ∫ RN λ(x) np(x) |∇u(x)| dx if u ∈ L(R ) ∩W 1,np(·)(RN ) +∞ otherwise, converges in the sense of Mosco to a functional ...
متن کاملVariational Principles in L∞ with Applications to Antiplane Shear and Plane Stress Plasticity
The yield set of a polycrystal is characterized by means of a variational principle in L∞ obtained via Γ-convergence of a class of power-law functionals in the setting of A-quasiconvexity. Our results apply, in particular, to the model cases of antiplane shear and plane stress plasticity. 2000 AMS Mathematics Classification Numbers: 35F99, 35J70, 49K20, 49S05, 74C05
متن کامل