论文标题
Annulus乘数和对具有阶跃电势的Helmholtz方程的限制吸收原理的应用
An annulus multiplier and applications to the Limiting absorption principle for Helmholtz equations with a step potential
论文作者
论文摘要
我们考虑helmholtz方程$-ΔU+v \，u-λ\，u = f $ on $ \ mathbb {r}^n $，其中潜在的$ v：\ mathbb {r}^n \ to \ mathbb {r mathbb {r} $在fime in of Half-spaces $ \ m m ift time in Iff time in Iff $ \ mathbb {r}^{n-1} \ times（0，\ infty）$。我们证明了$ l^p-l^q $ - 限制频率的吸收原理$λ> \ max \，v $借助傅立叶限制理论，并得出了线性和非线性helmholtz方程的非平凡溶液的存在。
We consider the Helmholtz equation $-Δu+V \, u - λ\, u = f $ on $\mathbb{R}^n$ where the potential $V:\mathbb{R}^n\to\mathbb{R}$ is constant on each of the half-spaces $\mathbb{R}^{n-1}\times (-\infty,0)$ and $\mathbb{R}^{n-1}\times (0,\infty)$. We prove an $L^p-L^q$-Limiting Absorption Principle for frequencies $λ>\max \, V$ with the aid of Fourier Restriction Theory and derive the existence of nontrivial solutions of linear and nonlinear Helmholtz equations.
