scholarly journals Integral representation and Γ-convergence of variational integrals withp(x)-growth

2002 ◽  
Vol 7 ◽  
pp. 495-519 ◽  
Author(s):  
Alessandra Coscia ◽  
Domenico Mucci
Keyword(s):  
Integral Representation ◽  
Variational Integrals ◽  
Γ Convergence

scholarly journals Γ-convergence of nonconvex integrals in Cheeger--Sobolev spaces and homogenization

2017 ◽  
Vol 10 (4) ◽  
pp. 381-405 ◽  
Author(s):  
Omar Anza Hafsa ◽  
Jean-Philippe Mandallena
Keyword(s):  
Calculus Of Variations ◽  
Sobolev Spaces ◽  
Variational Integrals ◽  
Γ Convergence

AbstractWe study Γ-convergence of nonconvex variational integrals of the calculus of variations in the setting of Cheeger–Sobolev spaces. Applications to relaxation and homogenization are given.

MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE

2006 ◽  
Vol 04 (01) ◽  
pp. 31-60 ◽  
Author(s):  
KARIM TRABELSI
Keyword(s):  
Integral Representation ◽  
Internal Energy ◽  
Elastic Membrane ◽  
Gamma Convergence ◽  
Two Dimensional ◽  
Incompressible Materials ◽  
Plate Models ◽  
Γ Convergence ◽  
Nonlinearly Elastic

In this paper, we derive nonlinearly elastic membrane plate models for hyperelastic incompressible materials using Γ-convergence arguments. We obtain an integral representation of the limit two-dimensional internal energy owing to a result of singular functionals relaxation due to Ben Belgacem [6].

scholarly journals On the relaxation of variational integrals in metric Sobolev spaces

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Omar Anza Hafsa ◽  
Jean-Philippe Mandallena
Keyword(s):  
Integral Representation ◽  
Calculus Of Variations ◽  
Sobolev Spaces ◽  
General Framework ◽  
Metric Measure Spaces ◽  
Representation Theorems ◽  
Differentiable Structure ◽  
Convex Case ◽  
Measure Spaces ◽  
Variational Integrals

AbstractWe give an extension of the theory of relaxation of variational integrals in classical Sobolev spaces to the setting of metric Sobolev spaces. More precisely, we establish a general framework to deal with the problem of finding an integral representation for “relaxed” variational functionals of variational integrals of the calculus of variations in the setting of metric measure spaces. We prove integral representation theorems, both in the convex and non-convex case, which extend and complete previous results in the setting of euclidean measure spaces to the setting of metric measure spaces. We also show that these integral representation theorems can be applied in the setting of Cheeger–Keith's differentiable structure.

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

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