Nonlinear elliptic equations with measure data in Orlicz spaces
UDC 517.5 In this article, we study the existence result of the unilateral problem\begin{gather*}Au-\mbox{div} (\Phi(x,u))+H(x,u,\nabla u)=\mu,\end{gather*}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 \...
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| Date: | 2021 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1290 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
In this article, we study the existence result of the unilateral problem\begin{gather*}Au-\mbox{div} (\Phi(x,u))+H(x,u,\nabla u)=\mu,\end{gather*}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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| DOI: | 10.37863/umzh.v73i12.1290 |