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:

We study variational problems with volume constraints (also called level set constraints) of the form

We consider a thin curved film made of a martensitic material. The behavior of the film is governed by a free energy composed of a bulk energy term and an interfacial energy term. We show that the minimizers of the free energy converge to the minimizers of an energy depending on a two-dimensional deformation and one Cosserat vector field when the thickness of the curved film goes to zero. using...

For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ-convergence theorem and show compactness up to translation in all L and certain Orlicz spaces for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher [1] for the coercive two-well case. The theorem has applications to a certain thin-f...

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via Γ-convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.

The current study aimed to research the chemical composition, antioxidant, herbicidal and antifungal effect three essential oils, as obtained from Thymus canoviridis Jalas., eriocalyx (Ronni.) Jalas. fallax Fisch. et C.A. Mey. Antioxidant capacities of oils were determined by 1.1dipheny1-2-picrylhydrazyl (DPPH) method. potential was tested in-vitro against Fusarium equiseti (Corda) Sacc., grami...

Thyme (Thymus vulgaris L.) is an important medicinal plant with highly valuable essential oils. In this study, effects of different fertilizer treatments and cuts on Thymus vulgaris L. was evaluated in 2008-2009. The research was conducted at Alborz Research Station, Research Institute of Forests and Rangelands, Karaj, Iran. The Experimental design was split plot in time in the form of a random...

the concept of  -semihyperring is a generalization of semiring, a generalization of semihyperring and a generalization of      -semiring. since the theory of ideals plays an important role in the theory of  - semihyperring, in this paper, we will make an intensive study of the notions of noetherian, artinian, simple and   regular      -semihyperrings. the bulk of this paper...