论文标题
在steklov-robin特征值问题上
On a Steklov-Robin eigenvalue problem
论文作者
论文摘要
在本文中，我们研究了环形域中拉普拉斯的steklov-robin特征值问题。更确切地说，我们考虑$ω=ω_0\ setMinus \ edminus \ edline {b} _ {r} $，其中$ b_ {r} $是以radius $ r> 0 $和$ r> 0 $和$ω_0\ subset \ subset \ subset \ subbb {r}^n $，$ n $ nip的开放式的，geq 2 $ queq 2 $ queq 2 $ queq 2 $ nist，是一个以radius $ r> r> 0 $> r> r> r> 0 $> r> r> r> r> r> r> r> r> $ \ OVERLINE {B} _ {R} \ subsetω_0$。我们在外部边界上施加了steklov条件，在内部边界上涉及正$ l^{\ infty} $ - 函数$β（x）$的罗宾条件。然后，我们研究了第一个特征值$σ_β（ω）$及其主要特性。特别是，当我们让$ l^1 $ norm的$β$和内球半径变化时，我们研究了$σ_β（ω）$的行为。此外，我们研究当$β$是无穷大的积极参数时，相应本征函数的渐近行为。
In this paper we study a Steklov-Robin eigenvalue problem for the Laplacian in annular domains. More precisely, we consider $Ω=Ω_0 \setminus \overline{B}_{r}$, where $B_{r}$ is the ball centered at the origin with radius $r>0$ and $Ω_0\subset\mathbb{R}^n$, $n\geq 2$, is an open, bounded set with Lipschitz boundary, such that $\overline{B}_{r}\subset Ω_0$. We impose a Steklov condition on the outer boundary and a Robin condition involving a positive $L^{\infty}$-function $β(x)$ on the inner boundary. Then, we study the first eigenvalue $σ_β(Ω)$ and its main properties. In particular, we investigate the behaviour of $σ_β(Ω)$ when we let vary the $L^1$-norm of $β$ and the radius of the inner ball. Furthermore, we study the asymptotic behaviour of the corresponding eigenfunctions when $β$ is a positive parameter that goes to infinity.
