A nonsolvable complex vector field with Hölder coefficients
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- by Howard Jacobowitz PDF
- Proc. Amer. Math. Soc. 116 (1992), 787-795 Request permission
Abstract:
It is known that the equation \[ \frac {{\partial u}}{{\partial t}} - \alpha (\xi ,t)\frac {{\partial u}}{{\partial \xi }} = f(\xi ,\tau )\] is solvable in a neighborhood of the origin provided Im $\alpha$ does not change sign and $\alpha$ is at least Lipschitz smooth. An example is given where solvability fails although $\alpha$ is of Hölder class $\lambda$ for all $0 < \lambda < 1$. Further, the only solutions to \[ \frac {{\partial u}}{{\partial t}} - \alpha (\xi ,t)\frac {{\partial u}}{{\partial \xi }} = 0\] are the constant functions.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 787-795
- MSC: Primary 35A07
- DOI: https://doi.org/10.1090/S0002-9939-1992-1107922-2
- MathSciNet review: 1107922