On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain
On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain
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有界域内拉普拉斯算子的广义Ventcel型边界条件
DOI：
10.1137/090756521
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
G. Vial
中科院分区：
文献类型：
--
作者：
V. Bonnaillie;M. Dambrine;F. Hérau;G. Vial
Ventcel边界条件是出现在渐近模型中的二阶微分条件。像罗宾边界条件，他们导致适定的变分问题下的一个系数的符号条件。然而，在一些作品中出现了违反这一条件的情况。这类问题的适定性仍然是开放的。本文在一般情况下证明了无符号条件下的Ventcel边值问题解的存在唯一性。然后我们考虑穿孔几何并给出消除类属性限制的条件。
Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to well-posed variational problems under a sign condition of a coefficient. Nevertheless, situations where this condition is violated appeared in several works. The well-posedness of such problems was still open. This manuscript establishes, in the generic case, the existence and uniqueness of the solution for the Ventcel boundary value problem without the sign condition. Then we consider perforated geometries and give conditions to remove the genericity restriction.