A similarity principle for complex vector fields and applications (Q2701674)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A similarity principle for complex vector fields and applications |
scientific article |
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A similarity principle for complex vector fields and applications (English)
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19 February 2001
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semilinear Cauchy problem
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locally solvable vector field
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This paper deals with a similarity principle for a class of non-elliptic, smooth complex vector fields in the plane \(\mathbb{R}^{2}\). The well-known condition \( (P) \) of Nirenberg-Treves is satisfied and therefore the vector fields under consideration are locally solvable. By using this principle a uniqueness theorem for a semilinear Cauchy problem is proved. In the special case when the vector field \(L\) is hypoelliptic rather precise results are shown in Corollary 4.4 and Propositions 4.7, 4.9.
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