Non trivial solutions of non-linear partial differential inequations and order cut-off
We derive necessary conditions on the space dimension such that a class of partial differential inequations admit a non trivial solution. We show that a nontrivial solution γ(γ : IR^N → IR^k) of this type of inequations may exist only if the dimension N is sufficiently large with respect to the mini...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1999-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(1)/137-154.pdf |
| Summary: | We derive necessary conditions on the space dimension such that a class of partial differential inequations admit a non trivial solution. We show that a nontrivial solution γ(γ : IR^N → IR^k) of this type of inequations may exist only if the dimension N is sufficiently large with respect to the minimal order
of the partial differential operator which is investigated. Furthermore, we prove that the cut-off property is actually governed by the number of variables which genuinely occur in the operator.
We briefly introduce a few motivations in statistical decision theory that lead to such inequations and dimension cut-off phenomenon. |
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| ISSN: | 1120-7183 2532-3350 |