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Proceedings of the American Mathematical Society

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

 
 

 

Weak equals strong for first-order linear pseudodifferential boundary value problems


Author: Leonard Sarason
Journal: Proc. Amer. Math. Soc. 39 (1973), 141-148
MSC: Primary 35S15; Secondary 35D10
DOI: https://doi.org/10.1090/S0002-9939-1973-0320567-5
MathSciNet review: 0320567
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Abstract: Weak solutions are shown to be strong for a class of boundary value problems for first-order linear differential equations with zero order pseudodifferential matrix coefficients. The operators have the form $ \chi {A_j}(x,D)\chi {D_j}\chi + \chi {A_0}\chi $, where $ \chi $ is the characteristic function of a domain $ G$. At the boundary, there are conditions on the coefficient $ {A_n}$ of normal differentiation, typically implying that $ {(\chi {A_n})^{ - 1}}$ is a bounded operator both on $ {L_2}(G)$ and on $ {H_1}(G)$. The proof uses tangential mollifiers and is also applied in a more abstract setting.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0320567-5
Keywords: Tangential mollifiers
Article copyright: © Copyright 1973 American Mathematical Society

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