Nonlinear elliptic equations with measure data in Orlicz spaces

  • A. Aberqi Sidi Mohammed Ben Abdellah Univ., Laboratory LAMA, Morocco
  • J. Bennouna Sidi Mohammed Ben Abdellah Univ., Laboratory LAMA, Morocco
  • M. Elmassoudi Sidi Mohammed Ben Abdellah Univ., Laboratory LAMA, Morocco
Keywords: Nonlinear elliptic problem, Unilateral problem, Weak solution, Orlicz spaces, Measure data


UDC 517.5

In this article, we study the existence result of the unilateral problem
Au-\mbox{div} (\Phi(x,u))+H(x,u,\nabla u)=\mu,
where $Au = -\mbox{div}(a(x,u,\nabla u))$ is a Leray–Lions operator defined on Sobolev–Orlicz space $D(A)\subset W_{0}^{1}L_{M}(\Omega),$ $\mu \in L^{1}(\Omega)+W^{-1}E_{\overline{M}}(\Omega),$ where $M$ and $\overline{M}$ are two complementary $N$-functions, the first and the second lower terms $\Phi$ and $H$ satisfies only the growth condition and any sign condition is assumed and $u\geq \zeta,$ where $\zeta$ is a measurable function.


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How to Cite
Aberqi, A., J. Bennouna, and M. Elmassoudi. “Nonlinear Elliptic Equations With Measure Data in Orlicz Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 12, Dec. 2021, pp. 1587 -11, doi:10.37863/umzh.v73i12.1290.
Research articles