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2012 Entropy Solution for Some $p(x)$-Quasilinear Problem with Right-Hand Side Measure
E. Azroul, M. B. Benboubker, M. Rhoudaf
Afr. Diaspora J. Math. (N.S.) 13(2): 23-44 (2012).


In this paper we study the existence of entropy solution for the following $p(x)$-quasilinear elliptic problem $$ \mbox{div}(a(x,u,\nabla u))+ g(x,u,\nabla u) = \mu$$ where the right-hand side $\mu$ is a measure, which admits a decomposition in $L^{1}(\Omega)+W^{-1,p'(x)}(\Omega)$ and $g(x,s,\xi)$ is a nonlinear term which has a growth condition with respect to $\xi$ and has no growth with respect to $s$ while satisfying a sign condition on $s$.


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E. Azroul. M. B. Benboubker. M. Rhoudaf. "Entropy Solution for Some $p(x)$-Quasilinear Problem with Right-Hand Side Measure." Afr. Diaspora J. Math. (N.S.) 13 (2) 23 - 44, 2012.


Published: 2012
First available in Project Euclid: 2 November 2012

zbMATH: 1272.35100
MathSciNet: MR3006751

Primary: 35J15
Secondary: 35J20 , 35J70 , 46E35

Keywords: entropy solution, truncations , Quasilinear elliptic equation , Sobolev spaces with variable exponent

Rights: Copyright © 2012 Mathematical Research Publishers

Vol.13 • No. 2 • 2012
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