On the anisotropic Orlicz spaces applied in the problems of continuum mechanics

Gwiazda, Piotr; Minakowski, Piotr; Świerczewska-Gwiazda, Agnieszka

doi:10.3934/dcdss.2013.6.1291

Cited by 8 publications

(12 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [26], the author established the existence of weak solutions for steady flows of non-Newtonian incompressible fluids with the help of a general x-dependent convex function in generalized Orlicz spaces. Later, Gwiazda et al [14] proved the existence of weak solutions to the generalized Stokes system in anisotropic Orlicz spaces.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Untitled

2021

Z. mat. fiz. anal. geom.

View full text Add to dashboard Cite

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Untitled

2021

Z. mat. fiz. anal. geom.

View full text Add to dashboard Cite

show abstract

“…Φpxq{|x| Ñ 0 when |x| Ñ 0. However, most of the results proved in [10] do not depend on this property. If Φpyq is an N 8 function which depends on |y| (Φpyq " Φp|y|q), then we say that Φ is radial.…”

Section: Anisotropic Orlicz and Orlicz-sobolev Spacesmentioning

confidence: 94%

“…For the theory of convex functions in general we suggest [7]. Note that, unlike in [10], we do not require that N 8 functions be superlinear near 0, i.e. Φpxq{|x| Ñ 0 when |x| Ñ 0.…”

Section: Anisotropic Orlicz and Orlicz-sobolev Spacesmentioning

confidence: 99%

Periodic solutions of Euler–Lagrange equations in an anisotropic Orlicz–Sobolev space setting

Mazzone¹,

Acinas²

2019

Rev. Un. Mat. Argentina

View full text Add to dashboard Cite

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations which include, among others, equations involving the p-Laplace operator and, more generally, the pp, qq-Laplace operator. We employ the direct method of the calculus of variations in the framework of anisotropic Orlicz-Sobolev spaces. These spaces appear to be useful in formulating a unified theory of existence of solutions for such a problem. * SECyT-UNRC, FCEyN-UNLPam and CONICET † SECyT-UNRC, FCEyN-UNLPam and UNSL 2010 AMS Subject Classification. Primary: 34C25. Secondary: 34B15.

show abstract

“…If ∆ 2 -condition fails, we lose numerous properties of the space L M (Q) like separability, reflexivity and many others, cf. [1,32] and particular [20] for generalized Orlicz spaces.…”

Section: Introductionmentioning

confidence: 99%

“…the truncations operator′ (T M (θ ε ))∇T M (θ ε ) • ∇φ dx dt + ′′ (T M (θ ε ))|∇T M (θ ε )| 2 φ dx dt = Q f ε S ′ (T M (θ ε ))φ dx dt. (A 20).…”

mentioning

confidence: 99%

Thermo-visco-elasticity for models with growth conditions in Orlicz spaces

Klawe¹

2016

TMNA

View full text Add to dashboard Cite

We study a quasi-static evolution of thermo-visco-elastic model. We act with external forces on non-homogeneous material body, which is a subject of our research. Such action may cause deformation of this body and may change its temperature. Mechanical part of the model contains two kinds of deformation: elastic and visco-elastic. Mechanical deformation is coupled with the temperature and they may influence each other. Since constitutive function on evolution of visco-elastic deformation depends on temperature, the visco-elastic properties of material also depend on temperature. We consider the thermodynamically complete model related to hardening rule with growth condition in generalized Orlicz spaces. We provide the proof of existence of solutions for such class of models.2000 Mathematics Subject Classification. 74C10, 35Q74, 74F05.

show abstract

On the anisotropic Orlicz spaces applied in the problems of continuum mechanics

Cited by 8 publications

References 11 publications

Untitled

Untitled

Periodic solutions of Euler–Lagrange equations in an anisotropic Orlicz–Sobolev space setting

Thermo-visco-elasticity for models with growth conditions in Orlicz spaces

Contact Info

Product

Resources

About