## African Diaspora Journal of Mathematics

### Entropy Solution for Some $p(x)$-Quasilinear Problem with Right-Hand Side Measure

#### Abstract

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 $s$.

#### Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 13, Number 2 (2012), 23-44.

Dates
First available in Project Euclid: 2 November 2012

Azroul, E.; Benboubker, M. B.; Rhoudaf, M. Entropy Solution for Some $p(x)$-Quasilinear Problem with Right-Hand Side Measure. Afr. Diaspora J. Math. (N.S.) 13 (2012), no. 2, 23--44. https://projecteuclid.org/euclid.adjm/1351864731