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1

Improved bounds for solutions of Φ-laplacians

Arriagada W., Huentutripay J.

Opuscula Mathematica

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2018

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Vol. 38, no. 6

765--777

EN

In this short paper we prove a parametric version of the Harnack inequality for Φ-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.

2

Remarks on the Sobolev type spaces of multifunctions

Kasperski A.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

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2015

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z. 5

53--60

EN

In this paper we introduce the spaces of multifunctions SX,pq and Xpq which correspond with the Sobolev space Wpq and the space of multifunctions Xmkc,φ,k,Y which correspond with the Orlicz-Sobolev space Wkφ. We study completeness of them. Also we give some theorems.

PL

W artykule wprowadzamy przestrzenie multifunkcji SXpq and Xpq, które odpowiadają przestrzeni Soboleva Wpq, oraz przestrzeń multifunkcji Xmkc,φ,k,Y , która odpowiada przestrzeni Orlicza-Soboleva Wkφ. Badamy zupełność tych przestrzeni. Podajemy także pewne twierdzenia dotyczące tych przestrzeni.

3

Effective energy integral functionals for thin films in the Orlicz-Sobolev space setting

Laskowski W., Nguyen H. T.

Demonstratio Mathematica

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2013

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Vol. 46, nr 3

585--604

EN

We consider an elastic thin film as a bounded open subset ω of R2. First, the effective energy functional for the thin film ω is obtained, by Γ-convergence and 3D-2D dimension reduction techniques applied to the sequence of re-scaled total energy integral functionals of the elastic cylinders (…) as the thickness ε goes to 0. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function for the elastic cylinders has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions (…) and (…) (that is equivalent to the reflexivity of Orlicz and Orlicz–Sobolev spaces generated by M). These results extend results of H. Le Dret and A. Raoult for the case M(t) = (…) for some (…).

4

On a class of nonhomogenous quasilinear problems in Orlicz-Sobolev spaces

Souayah A. K.

Opuscula Mathematica

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2012

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Vol. 32, no. 4

731-750

EN

We study the nonlinear boundary value problem [formula], where Ω is a bounded domain in RN with smooth boundary, λ, μ are positive real numbers, q and α are continuous functions and a1,a2 are two mappings such that a1 (/t/)t; a2(/t/)t; are increasing homeomorphisms from R to R. The problem is analysed in the context of Orlicz-Soboev spaces. First we show the existence of infinitely many weak solutions for any λ, μ > 0. Second we prove that for any μ > 0, there exists λ* sufficiently small, and λ* large enough such that for any λ ∈ (0, λ*) ∪ (λ*, ∞), the above nonhomogeneous quasilinear problem has a non-trivial weak solution.

5

Approximation by functions in C0∞(Ω) in Orlicz - Sobolev spaces

Liskowski M.

Fasciculi Mathematici

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2005

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Nr 36

73-82

EN

The results presented in this paper concern the identity of spaces Wk, M Ω and Wk, M Ω generated by &phi-functions M with parameter for some class domains Ω ⊂ Rn and they are the extension of analogous results for clasical Sobolev spaces. The problem of approximation of elements in Wk, M Ω by smooth functions on various domains Ω ⊂ Rn were investigated by different authors for classic Sobolev spaces with integer values of k as well as for some generalization of Sobolev space to the case of noninteger values k (see e.g. N. Meyers and J. Serrin [11] in the case M(u) =up, p> 1; T. K. Donaldson and N. S. Trudinger [2], when M is arbitrary N-function; H. Hudzik [3], [4], [5], [6]. [7], when M is TV-function which depends on parameter; M. Liskowski [9] [10] for some family of generalized Orlicz-Sobolev space, when k is noninteger and M is N-function with parameter).

6

Interpolation inequalities in Orlicz-Sobolev space

Liskowski M.

Fasciculi Mathematici

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1999

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Nr 30

99-106

EN

We consider the problem of detennining upper bounds for nonns of functions from Orlicz-Sobolev space[...], [...] in tenns of nonns of the space [...] and Orlicz space. The interpolation inequalities of this type are well-known for classical Sobolev spaces [...], [...]and also [1].