Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A nonsolvable complex vector field with Hölder coefficients


Author: Howard Jacobowitz
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is known that the equation

$\displaystyle \frac{{\partial u}}{{\partial t}} - \alpha (\xi ,t)\frac{{\partial u}}{{\partial \xi }} = f(\xi ,\tau )$

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

$\displaystyle \frac{{\partial u}}{{\partial t}} - \alpha (\xi ,t)\frac{{\partial u}}{{\partial \xi }} = 0$

are the constant functions.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35A07

Retrieve articles in all journals with MSC: 35A07


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1107922-2
Article copyright: © Copyright 1992 American Mathematical Society