带Hardy位势的分数阶拉普拉斯算子的低阶项
Lower order term for the fractional Laplacian with a Hardy potential
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中文总结 AI 辅助
本文研究带Hardy位势的分数阶拉普拉斯半线性椭圆方程，在权函数g的特定可积性条件下，证明了对任意实数λ解的存在性，并获得了解的正则性结果。
中文摘要 AI 辅助
本文研究$\u211d^N$（$N>2s$）中有界区域$Ω$内涉及分数阶拉普拉斯算子的半线性椭圆方程：$(-Δ)^s u+ g|u|^{p-1}u= λ\frac{u}{|x|^{2s}}+f(x)$，其在$\u211d^N\setminus Ω$上满足零Dirichlet条件，其中$0<g\in L_{loc}^1(Ω)$，$p>1$，$f\in L^{(p+1)/p}_g(Ω)$。在$g$的特定可积性条件下，证明了对任意$λ\in\u211d$解均存在，还得到了解的正则性。
英文摘要
This paper is concerned with the following semilinear elliptic equation involving the fractional Laplacian: $$(-Δ)^s u+ g|u|^{p-1}u= λ\frac{u}{|x|^{2s}}+f(x),$$ in a bounded domain $Ω$ of $\mathbb{R}^N\,(N>2s)$, subject to the zero Dirichlet condition in $\mathbb{R}^N\setminus Ω$, where $0<g\in L_{loc}^1(Ω)$, $p>1$ and $f\in L^{(p+1)/p}_g(Ω)$. Under certain integrability condition on $g$, the existence of solution is proven for every $λ\in \mathbb{R}$. Moreover, the regularity of solution is also obtained.
