论文标题
广义Orlicz-sobolev空间中的扩展
Extension in generalized Orlicz--Sobolev spaces
论文作者
论文摘要
我们研究了扩展运算符的存在$λ\ colon w^{1，φ}（ω）\ to w^{1，ψ}（\ Mathbb {r}^n）$。我们假设$φ\在φ_\ mathrm {w}（ω）中的$概括了Orlicz的增长，$ψ\ inφ__\ Mathrm {w}（\ Mathbb {r}^n）$是$ $ q $的扩展名，是$ c \ subset \ subset \ subset \ subset \ mathbb $ domain $ nis $ an $特殊情况包括经典常数指数案例，Orlicz情况，可变指数案例和双相案例。
We study the existence of an extension operator $Λ\colon W^{1,φ}(Ω)\to W^{1,ψ}(\mathbb{R}^n)$. We assume that $φ\in Φ_\mathrm{w}(Ω)$ has generalized Orlicz growth, $ψ\in Φ_\mathrm{w}(\mathbb{R}^n)$ is an extension of $φ$, and that $Ω\subset\mathbb{R}^n$ is an $(ε,δ)$-domain. Special cases include the classical constant exponent case, the Orlicz case, the variable exponent case, and the double phase case.
