论文标题
Orthropic $ p $ -laplace eigenvalue steklov类型的$ p \ to+\ infty $
The orthotropic $p$-Laplace eigenvalue problem of Steklov type as $p\to+\infty$
论文作者
论文摘要
我们研究$ \ infty- $ orthropic laplace操作员的steklov特征值问题，该操作员在$ \ mathbb {r}^n $ convex集中定义，并带有$ n \ geq2 $，考虑到$ p \ to+p \ to+p \ forsteklov for p p-p-p-$ $ p-p-p-p- $ p-p-p-p-p-p-p-p-p- $或lastroproc lthloc lthloc lthloc l.我们发现在粘度意义上满足的极限问题和第一个非微不足道特征值的几何表征。此外，我们证明了凸套装之间的Brock-Weinstock和Weinstock类型的不等式，并指出，一旦我们修复了体积或Anisotropicticeter，一旦我们固定了steklov $ \ Infty- $正交的Laplacian的第一个非琐事特征值。
We study the Steklov eigenvalue problem for the $\infty-$orthotropic Laplace operator defined on convex sets of $\mathbb{R}^N$, with $N\geq2$, considering the limit for $p\to+\infty$ of the Steklov problem for the $p-$orthotropic Laplacian. We find a limit problem that is satisfied in the viscosity sense and a geometric characterization of the first non trivial eigenvalue. Moreover, we prove Brock-Weinstock and Weinstock type inequalities among convex sets, stating that the ball in a suitable norm maximizes the first non trivial eigenvalue for the Steklov $\infty-$orthotropic Laplacian, once we fix the volume or the anisotropic perimeter.
