ABSTRACT

In this paper, we investigate the existence theorem of entropy solutions for nonlinear elliptic problem of the type $-\mathrm{div}(a(x,u,\mathrm{\nabla }u)+\mathrm{\Phi }(x,u))+g(x,u,\mathrm{\nabla }u)=\mu$ in Ω, in the setting of Musielak-Orlicz spaces. The lower order term Φ verifies the natural growth condition, the nonlinearity g has a natural growth with respect to its third argument and with sign condition, no ${\mathrm{\Delta }}_2$-condition is assumed on the Musielak function, and the datum μ is assumed to belong to $L^1(\mathrm{\Omega })+W^{-1}{E}_{\overline{\phi }}(\mathrm{\Omega })$.

中文翻译：

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Musielak-Orlicz空间中具有测度数据的强非线性椭圆问题

摘要

在本文中，我们研究了非线性椭圆型问题的熵解的存在性定理 $-\mathrm{div}（\mathrm{一种}（X，ü，\mathrm{\nabla }ü）+\mathrm{\Phi }（X，ü））+G（X，ü，\mathrm{\nabla }ü）=\mu$在Musielak-Orlicz空间的设置中以Ω为单位。低阶项Φ验证了自然增长条件，非线性g相对于其第三自变量和带符号条件具有自然增长，否${\mathrm{\Delta }}_2$Musielak函数上假设--条件，并且假定数据μ属于${\mathrm{大号}}^{\mathrm{1个}}（\mathrm{\Omega }）+{\mathrm{w\; ^}}^{-\mathrm{1个}}{Ë}_{\overline{\phi }}（\mathrm{\Omega }）$。