caa a22 4500 605460930 CHVBK 20210128100241.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10114-015-3555-7 doi (NATIONALLICENCE)springer-10.1007/s10114-015-3555-7 Entropy and renormalized solutions for nonlinear elliptic problem involving variable exponent and measure data [Elektronische Daten] [Mohamed Benboubker, Houssam Chrayteh, Mostafa El Moumni, Hassane Hjiaj] We give an existence result of entropy and renormalized solutions for strongly nonlinear elliptic equations in the framework of Sobolev spaces with variable exponents of the type: $$- div(a(x,u,\nabla u) + \varphi (u)) + g(x,u,\nabla u) = \mu ,$$ where the right-hand side belongs to L 1(Ω) + W −1,p′(x)(Ω), -div(a(x, u,∇u)) is a Leray-Lions operator defined from W −1,p′(x)(Ω) into its dual and φ ∈ C 0(ℝ,ℝ N ). The function g(x, u,∇u) is a non linear lower order term with natural growth with respect to |∇u| satisfying the sign condition, that is, g(x, u,∇u)u ≥ 0. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2014 Nonlinear elliptic problem nationallicence Sobolev spaces nationallicence variable exponent nationallicence entropy solution nationallicence renormalized solution nationallicence measure data nationallicence Benboubker Mohamed National School of Applied Sciences, Abdelmalek Essaadi University, BP 2222, M'hannech Tétouan, Morocco aut Chrayteh Houssam Faculty of Science, Department of Mathematics and Computer Science, Beirut Arab University, Debbieh, Lebanon aut El Moumni Mostafa Laboratory LAMA, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, B.P 1796, Atlas Fez, Morocco aut Hjiaj Hassane Laboratory LAMA, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, B.P 1796, Atlas Fez, Morocco aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/1(2015-01-01), 151-169 1439-8516 31:1<151 2015 31 10114 https://doi.org/10.1007/s10114-015-3555-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-3555-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Benboubker Mohamed National School of Applied Sciences, Abdelmalek Essaadi University, BP 2222, M'hannech Tétouan, Morocco aut NATIONALLICENCE 700 1- Chrayteh Houssam Faculty of Science, Department of Mathematics and Computer Science, Beirut Arab University, Debbieh, Lebanon aut NATIONALLICENCE 700 1- El Moumni Mostafa Laboratory LAMA, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, B.P 1796, Atlas Fez, Morocco aut NATIONALLICENCE 700 1- Hjiaj Hassane Laboratory LAMA, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, B.P 1796, Atlas Fez, Morocco aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/1(2015-01-01), 151-169 1439-8516 31:1<151 2015 31 10114