External approximation of first order variational  problems
via W-1,p estimates

Cesare Davini; Roberto Paroni

Displaying similar documents to “External approximation of first order variational problems via W-1,p estimates”

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...

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 Caccioppoli-type and Poincaré inequalities with Orlicz norms.

Agarwal, Ravi P., Ding, Shusen (2010)

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.

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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Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian, Gilles A. Francfort (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as...

Inequality of Poincaré-Friedrich's type on $L^{p}$ spaces.

Dostanić, Milutin R. (2005)

Matematichki Vesnik

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Solvability of the Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains.

Boccia, Serena, Monsurrò, Sara, Transirico, Maria (2008)

Boundary Value Problems [electronic only]

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Finite volume schemes for fully non-linear elliptic equations in divergence form

Jérôme Droniou (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the $p$ -laplacian kind: $- div (| \nabla u |^{p - 2} \nabla u) = f$ (with $1 < p < \infty$ ). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.