
Softcover ISBN: | 978-2-85629-928-9 |
Product Code: | SMFMEM/166 |
List Price: | $52.00 |
AMS Member Price: | $41.60 |

Softcover ISBN: | 978-2-85629-928-9 |
Product Code: | SMFMEM/166 |
List Price: | $52.00 |
AMS Member Price: | $41.60 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 166; 2020; 94 ppMSC: Primary 35; 82
Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let \(V\) denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. The authors consider the operator \(\mathcal{A}_{h}=-h^{2}\Delta+iV\) in the semi-classical limit \(h\to 0\) and obtain both the asymptotic behavior of the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. They extend here previous results obtained for potentials for which the set where the current (or \(\nabla V\)) is normal to the boundary is discrete, in contrast with the present case where \(V\) is constant along the conducting surfaces.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let \(V\) denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. The authors consider the operator \(\mathcal{A}_{h}=-h^{2}\Delta+iV\) in the semi-classical limit \(h\to 0\) and obtain both the asymptotic behavior of the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. They extend here previous results obtained for potentials for which the set where the current (or \(\nabla V\)) is normal to the boundary is discrete, in contrast with the present case where \(V\) is constant along the conducting surfaces.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.