Strongly nonlinear Gagliardo–Nirenberg inequality in Orlicz spaces and Boyd indices

2017 ◽  
Vol 28 (1) ◽  
pp. 119-141 ◽  
Author(s):  
Claudia Capone ◽  
Alberto Fiorenza ◽  
Agnieszka Kałamajska
Keyword(s):  
Orlicz Spaces ◽  
Boyd Indices ◽  
Strongly Nonlinear ◽  
Nirenberg Inequality

Strongly nonlinear parabolic inequality in orlicz spaces via a sequence of penalized equations

2015 ◽  
Vol 26 (7-8) ◽  
pp. 1669-1695 ◽  
Author(s):  
Y. Akdim ◽  
J. Bennouna ◽  
M. Mekkour ◽  
H. Redwane
Keyword(s):  
Orlicz Spaces ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
Parabolic Inequality

Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

2012 ◽  
Vol 98 (3) ◽  
pp. 253-263 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Orlicz Spaces ◽  
Riesz Potentials ◽  
Nirenberg Inequality

scholarly journals Existence of solutions for some strongly nonlinear parabolic problems involving lower order terms in divergence form in Musielak-Orlicz spaces

2019 ◽  
Vol 38 (6) ◽  
pp. 99-126
Author(s):  
Abdeslam Talha ◽  
Abdelmoujib Benkirane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Strongly Nonlinear ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this work, we prove an existence result of entropy solutions in Musielak-Orlicz-Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data.

The Maximal Operator in Variable Spaces 𝐿 𝑝(·)(Ω, ρ) with Oscillating Weights

2006 ◽  
Vol 13 (1) ◽  
pp. 109-125 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Natasha Samko ◽  
Stefan Samko
Keyword(s):  
Lipschitz Condition ◽  
Maximal Operator ◽  
Orlicz Spaces ◽  
Weight Functions ◽  
Power Functions ◽  
Index Numbers ◽  
Boyd Indices ◽  
Open Set ◽  
Class Weight ◽  
Young Functions

Abstract We study the boundedness of the maximal operator in the spaces 𝐿 𝑝(·)(Ω, ρ) over a bounded open set Ω in 𝑅𝑛 with the weight , where 𝑤𝑘 has the property that belongs to a certain Zygmund-type class. Weight functions 𝑤𝑘 may oscillate between two power functions with different exponents. It is assumed that the exponent 𝑝(𝑥) satisfies the Dini–Lipschitz condition. The final statement on the boundedness is given in terms of index numbers of functions 𝑤𝑘 (similar in a certain sense to the Boyd indices for the Young functions defining Orlicz spaces).

scholarly journals Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces

2021 ◽  
Vol 55 (1) ◽  
pp. 43-70
Author(s):  
Abdeslam Talha ◽  
Mohamed Saad Bouh Elemine Vall
Keyword(s):  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Growth Conditions ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Unilateral Problems ◽  
Sign Conditions ◽  
Lower Order Terms

In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.

scholarly journals Existence of solutions for elliptic equations having natural growth terms in Orlicz spaces

2004 ◽  
Vol 2004 (12) ◽  
pp. 1031-1045 ◽  
Author(s):  
A. Elmahi ◽  
D. Meskine
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Natural Growth Terms

Existence result for strongly nonlinear elliptic equation with a natural growth condition on the nonlinearity is proved.

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