Hausdorff measure of critical sets of solutions to magnetic Schrödinger equations (Q532559)
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scientific article; zbMATH DE number 5884581
| Language | Label | Description | Also known as |
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| English | Hausdorff measure of critical sets of solutions to magnetic Schrödinger equations |
scientific article; zbMATH DE number 5884581 |
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Hausdorff measure of critical sets of solutions to magnetic Schrödinger equations (English)
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5 May 2011
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This paper is concerned with a class of Schrödinger equations involving a magnetic field and subject to a Neumann boundary condition. The main result in the present paper establishes a global 1-dimensional Hausdorff measure estimate for the critical set of complex-valued solutions. The proof combines variational arguments with related \(L^p\) and Schauder estimates.
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superconductivity
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Hausdorff measure
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magnetic Schrödinger equation
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