论文标题
Dirichlet到Neumann操作员的磁性不平等
The diamagnetic inequality for the Dirichlet-to-Neumann operator
论文作者
论文摘要
让$ω$成为R D与Lipschitz边界$γ$的有限域。我们在L 2（$γ$）上定义了与第二阶椭圆运算符a = -d k，j = 1 $ \ partial $ k（c kl $ \ partial $ l） + d k = 1 b k $ \ partial $ k- $ k- $ k $ k $ k $ k $ k $ k $ \ times for for for for pore a pre a prection。在N.的半群中。我们应用此标准来证明L 2（$γ$）上此类运营商的磁性不平等。
Let $Ω$ be a bounded domain in R d with Lipschitz boundary $Γ$. We define the Dirichlet-to-Neumann operator N on L 2 ($Γ$) associated with a second order elliptic operator A = -- d k,j=1 $\partial$ k (c kl $\partial$ l) + d k=1 b k $\partial$ k -- $\partial$ k (c k $\times$) + a 0. We prove a criterion for invariance of a closed convex set under the action of the semigroup of N. Roughly speaking, it says that if the semigroup generated by --A, endowed with Neumann boundary conditions, leaves invariant a closed convex set of L 2 ($Ω$), then the 'trace' of this convex set is invariant for the semigroup of N. We use this invariance to prove a criterion for the domination of semigroups of two Dirichlet-to-Neumann operators. We apply this criterion to prove the diamagnetic inequality for such operators on L 2 ($Γ$).
