0000000000937477

AUTHOR

Elvira Zappale

showing 7 related works from this author

3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization

2012

A 3D-2D dimension reduction for a nonlinear optimal design problem with a perimeter penalization is performed in the realm of $\Gamma$-convergence, providing an integral representation for the limit functional.

Optimal designMathematical optimizationIntegral representationdimension reductionDimensionality reductionGeneral Medicinedimension reduction; optimal designPerimeterNonlinear systemMathematics - Analysis of PDEsDimensional reductionConvergence (routing)FOS: MathematicsApplied mathematicsLimit (mathematics)optimal designDimensional reductionMathematicsAnalysis of PDEs (math.AP)
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Dimensional reduction for energies with linear growth involving the bending moment

2008

A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.

Mathematics(all)Asymptotic analysis49J45 49Q20 74K35dimension reductionGeneral Mathematics01 natural sciencesMathematics - Analysis of PDEsTangent measures; bending moments; dimension reductionFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsScalingFunctions of bounded variationMathematicsDeformation (mechanics)Applied Mathematics010102 general mathematicsMathematical analysisTangent measures010101 applied mathematicsNonlinear systemΓ-convergenceDimensional reductionBounded variationBending momentbending momentsVector fieldMSC: 49J45; 49Q20; 74K35Analysis of PDEs (math.AP)
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Relaxation of certain integral functionals depending on strain and chemical composition

2012

We provide a relaxation result in $BV \times L^q$, $1\leq q < +\infty$ as a first step towards the analysis of thermochemical equilibria.

RelaxationStrain (chemistry)Applied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisThermodynamics02 engineering and technologyRelaxation; functions of bounded variation; quasiconvexity.01 natural sciencesquasiconvexityMathematics - Analysis of PDEsfunctions of bounded variation0202 electrical engineering electronic engineering information engineeringFOS: MathematicsRelaxation (physics)020201 artificial intelligence & image processing0101 mathematicsPhysics::Chemical PhysicsChemical compositionMathematicsAnalysis of PDEs (math.AP)
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Relaxation of periodic and nonstandard growth integrals by means of two-scale convergence

2019

An integral representation result is obtained for the variational limit of the family functionals $\int_{\Omega}f\left(\frac{x}{\varepsilon}, Du\right)dx$, as $\varepsilon \to 0$, when the integrand $f = f (x,v)$ is a Carath\'eodory function, periodic in $x$, convex in $v$ and with nonstandard growth.

PhysicsIntegral representationRegular polygonScale (descriptive set theory)homomgenizationFunction (mathematics)two scale convergencehomomgenization; two scale convergencehomomgenization two scale convergenceMathematics - Analysis of PDEsConvergence (routing)FOS: MathematicsRelaxation (physics)Limit (mathematics)Analysis of PDEs (math.AP)Mathematical physics
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Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems of Fracture Mechanics

2009

We provide some lower semicontinuity results in the space of special functions of bounded deformation for energies of the type $$ %\int_\O {1/2}({\mathbb C} \E u, \E u)dx + \int_{J_{u}} \Theta(u^+, u^-, \nu_{u})d \H^{N-1} \enspace, \enspace [u]\cdot \nu_u \geq 0 \enspace {\cal H}^{N-1}-\hbox{a. e. on}J_u, $$ and give some examples and applications to minimum problems. \noindent Keywords: Lower semicontinuity, fracture, special functions of bounded deformation, joint convexity, $BV$-ellipticity.

Mathematics - Analysis of PDEsFOS: MathematicsFOS: Physical sciences49J45 74A45 74R10Mathematical Physics (math-ph)Mathematical PhysicsAnalysis of PDEs (math.AP)
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Dimension reduction for $-Delta_1$

2012

A 3D-2D dimension reduction for $-\Delta_1$ is obtained. A power law approximation from $-\Delta_p$ as $p \to 1$ in terms of $\Gamma$- convergence, duality and asymptotics for least gradient functions has also been provided.

dimension reduction; gamma convergence; duality; functions of bounded variation; 1-laplacianMathematics - Analysis of PDEsdimension reductionfunctions of bounded variationdualitygamma convergence1-laplacian
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Lower semicontinuous envelopes in $w^{1,1}\times l^p$

2012

It is studied the lower semicontinuity of functionals of the type $\int_\Omega f(x,u,v, \nabla u)dx$ with respect to the $(W^{1,1}\times L^p)$-weak \ast topology. Moreover in absence of lower semicontinuity, it is also provided an integral representation in $W^{1,1} \times L^p$ for the lower semicontinuous envelope.

Mathematics - Analysis of PDEsFOS: MathematicsAnalysis of PDEs (math.AP)
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