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Proceedings of the American Mathematical Society

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

 

 

On local solvability of pseudo-differential equations


Author: A. Menikoff
Journal: Proc. Amer. Math. Soc. 43 (1974), 149-154
MSC: Primary 47G05; Secondary 35S05
DOI: https://doi.org/10.1090/S0002-9939-1974-0338844-1
MathSciNet review: 0338844
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Abstract: A sufficient condition for the local solvability of the equation $ {u_t} - A(x,t,{D_x})u = f(x,t)$ is proved, where $ A$ is a first order pseudo-differential operator with real symbol. This is a special case of the local solvability conjecture of Nirenberg and Treves.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0338844-1
Keywords: Local solvability, pseudo-differential operators, localization, Gårding's inequality, a priori estimates, Hörmander's partition of unity
Article copyright: © Copyright 1974 American Mathematical Society