Distributions for which div v = F has a continuous solution |
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| Authors: | Thierry De Pauw Washek F Pfeffer |
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| Institution: | 1. Université Catholique de Louvain, Département de Mathématiques, Chemin du Cyclotron, 2, B‐1348 Louvain‐la‐Neuve, Belgium;2. University of California, Davis, Department of Mathematics, One Shields Avenue, Davis, CA 95616 |
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| Abstract: | The equation div v = F has a continuous weak solution in an open set U ? ?m if and only if the distribution F satisfies the following condition: the F(φi) converge to 0 for every sequence {φi} of test functions such that the support of each φi is contained in a fixed compact subset of U, and in the L1 norm, {φi} converges to 0 and {?φi} is bounded. © 2007 Wiley Periodicals, Inc. |
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