An optimal design problem with non-standard growth and no concentration effects
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Publication:5075588
DOI10.3233/ASY-211711zbMath1489.35272arXiv2007.01863OpenAlexW3166994729MaRDI QIDQ5075588
Elvira Zappale, Ana Cristina Barroso
Publication date: 16 May 2022
Published in: Asymptotic Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.01863
convexitydimension reductiondamagesets of finite perimeternon-standard growth conditionsoptimal designthin films
Nonlinear elasticity (74B20) Fracture and damage (74R99) Thin films (74K35) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09) PDE constrained optimization (numerical aspects) (49M41)
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Relaxation for an optimal design problem inBD(Ω), Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth
Cites Work
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- The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models
- On variational problems and nonlinear elliptic equations with nonstandard growth conditions
- Variable Lebesgue spaces. Foundations and harmonic analysis
- Lebesgue and Sobolev spaces with variable exponents
- Bending moment in membrane theory
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Partial regularity for optimal design problems involving both bulk and surface energies
- Jensen's inequality in the calculus of variations
- An optimal design problem with perimeter penalization
- Relaxation of multiple integrals below the growth exponent
- A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
- Orlicz spaces and generalized Orlicz spaces
- Relaxation of convex functionals: the gap problem
- The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
- 3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization
- Fracture models as \(\Gamma\)-limits of damage models
- Relaxation for optimal design problems with non-standard growth
- A necessary and sufficient condition for lower semicontinuity
- 3D-2D Asymptotic Analysis for Inhomogeneous Thin Films
- Optimal design and relaxation of variational problems, III
- Optimal design and relaxation of variational problems, I
- Optimal design and relaxation of variational problems, II
- The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent
- On Lower Semicontinuity of Integral Functionals. I
- 3D-2D asymptotic analysis of an optimal design problem for thin films
- Minimizers for a double-well problem with affine boundary conditions
- Integral representation and Γ-convergence of variational integrals withp(x)-growth
- Fracture and plastic models as Γ-limits of damage models under different regimes
- Concentration versus Oscillation Effects in Brittle Damage
- Strict interior approximation of sets of finite perimeter and functions of bounded variation
- RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY
- Integral Functionals and the Gap Problem: Sharp Bounds for Relaxation and Energy Concentration
- Direct methods in the calculus of variations