%0 Journal Article %1 ingerman1998characterization %A Ingerman, David %A Morrow, James A. %D 1998 %J SIAM Journal on Mathematical Analysis %K Dirichlet_to_Neumann_map PDE effective_resistance %N 1 %P 106-115 %R 10.1137/S0036141096300483 %T On a Characterization of the Kernel of the Dirichlet-to-Neumann Map for a Planar Region %U /brokenurl# http://dx.doi.org/10.1137/S0036141096300483 %V 29 %X We will show that the Dirichlet-to-Neumann map Λ for the electrical conductivity equation on a simply connected plane region has an alternating property, which may be considered as a generalized maxi- mum principle. Using this property, we will prove that the kernel, K, of n(n+1) Λ satisfies a set of inequalities of the form (−1) 2 det K(x i , y j ) > 0. We will show that these inequalities imply Hopf’s lemma for the con- ductivity equation. We will also show that these inequalities imply the alternating property of a kernel.

@article{ingerman1998characterization, abstract = {We will show that the Dirichlet-to-Neumann map Λ for the electrical conductivity equation on a simply connected plane region has an alternating property, which may be considered as a generalized maxi- mum principle. Using this property, we will prove that the kernel, K, of n(n+1) Λ satisfies a set of inequalities of the form (−1) 2 det K(x i , y j ) > 0. We will show that these inequalities imply Hopf’s lemma for the con- ductivity equation. We will also show that these inequalities imply the alternating property of a kernel.}, added-at = {2015-10-04T03:58:30.000+0200}, author = {Ingerman, David and Morrow, James A.}, biburl = {https://www.bibsonomy.org/bibtex/2d9fa55bc23dc3e61df9bac46f7ab636c/peter.ralph}, doi = {10.1137/S0036141096300483}, eprint = {http://dx.doi.org/10.1137/S0036141096300483}, interhash = {7186b4875fc55aa7ae6ffe963db7d22c}, intrahash = {d9fa55bc23dc3e61df9bac46f7ab636c}, journal = {SIAM Journal on Mathematical Analysis}, keywords = {Dirichlet_to_Neumann_map PDE effective_resistance}, number = 1, pages = {106-115}, timestamp = {2015-10-04T04:02:37.000+0200}, title = {On a Characterization of the Kernel of the {Dirichlet}-to-{Neumann} Map for a Planar Region}, url = {/brokenurl# http://dx.doi.org/10.1137/S0036141096300483 }, volume = 29, year = 1998 }