This note completely resolves the asymptotic development of order 2 by Γ-convergence of the mass-constrained Cahn–Hilliard functional, by showing that one of the critical assumptions of the authors’ previous work [10] is unnecessary.

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 diffuse extragalactic γ-ray background in the MeV region is believed to be due to photons from radioactivity produced in supernovae throughout the history of galaxies in the universe. In particular, γ-ray line emission from the decay chain 56Ni→ 56Co → 56Fe provides the dominant photon source (Clayton & Silk 1969). Although iron synthesis occurs in all types of supernovae, the contribution ...

木村雄一郎,本 田嘉秀:近 畿大 学理工学 部原子炉 工学科,東 大阪市,〒577 Comparative studies on the uptake and elimination of radionuclides, 6OCo, 131I, 137Cs, 141Ce and 106Ru by the advanced fry and the fingerlings of rainbow trout were conducted under laboratory conditions. The general patterns of uptake of 60Co, 131I, 114Ce, 106RuNO-nitro and -binuclear complexes by both the advanced fry and the fingerlings were similar t...

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...