Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian; Gilles A. Francfort

Displaying similar documents to “Spatial heterogeneity in 3D-2D dimensional reduction”

External approximation of first order variational problems estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving $W^{- 1, p}$ norms obtained by Nečas and on the general framework of -convergence theory.

Weak solutions for elliptic systems with variable growth in Clifford analysis

Yongqiang Fu, Binlin Zhang (2013)

Czechoslovak Mathematical Journal

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In this paper we consider the following Dirichlet problem for elliptic systems: $\begin{matrix} \bar{D A (x, u (x), D u (x))} = & B (x, u (x), D u (x)), x \in Ω, u (x) = & 0, x \in \partial Ω, \end{matrix}$ where $D$ is a Dirac operator in Euclidean space, $u (x)$ is defined in a bounded Lipschitz domain $Ω$ in $ℝ^{n}$ and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the...

New versions of the Nyman-Beurling criterion for the Riemann hypothesis.

Báez-Duarte, Luis (2002)

International Journal of Mathematics and Mathematical Sciences

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The scalar Oseen operator $- Δ + \partial / \partial x_{1}$ in $ℝ^{2}$

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in $L^{p}$ theory.

Global integrability of the Jacobian of a composite mapping.

Ding, Shusen, Liu, Bing (2006)

Journal of Inequalities and Applications [electronic only]

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-convergence of functionals on divergence-free fields

Nadia Ansini, Adriana Garroni (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of -convergence. We prove that the -limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the -limit is also stable under volume constraint and various type of boundary conditions.

Displaying similar documents to “Spatial heterogeneity in 3D-2D dimensional reduction”

External approximation of first order variational problems estimates

Weak solutions for elliptic systems with variable growth in Clifford analysis

New versions of the Nyman-Beurling criterion for the Riemann hypothesis.

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Global integrability of the Jacobian of a composite mapping.

-convergence of functionals on divergence-free fields

The scalar Oseen operator $- Δ + \partial / \partial x_{1}$ in $ℝ^{2}$