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Proceedings of the American Mathematical Society

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

 

 

Coercive inequalities for certain classes of bounded regions


Author: James M. Newman
Journal: Proc. Amer. Math. Soc. 32 (1972), 120-126
MSC: Primary 35B45
DOI: https://doi.org/10.1090/S0002-9939-1972-0296480-8
MathSciNet review: 0296480
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Abstract: In this paper, sufficient conditions are given for the coerciveness of formally positive integrodifferential forms over complex-valued functions satisfying zero boundary conditions in certain bounded domains in $ {R_2}$; the boundaries need not be smooth. This work extends results given by the author in Comm. Pure Appl. Math., November 1969.

In addition, sufficient conditions and partial necessity conditions are given for coercive-type inequalities involving differential operators in the Hölder norm; here the results hold for complex-valued functions with no boundary conditions; the regions are bounded subdomains of $ {R_n}$ having the cone property.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296480-8
Keywords: Coerciveness, formally positive integrodifferential forms, Hölder norm, piecewise-smooth boundaries, sectors in the plane, finite partition of unity, Garding's inequality, interpolation lemma, cone property, uniformly collectively elliptic, patching technique
Article copyright: © Copyright 1972 American Mathematical Society