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Transactions of the American Mathematical Society

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Hypoellipticity of certain degenerate elliptic boundary value problems


Author: Yakar Kannai
Journal: Trans. Amer. Math. Soc. 217 (1976), 311-328
MSC: Primary 35H05
DOI: https://doi.org/10.1090/S0002-9947-1976-0407436-4
MathSciNet review: 0407436
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Abstract: The concept of hypoellipticity for degenerate elliptic boundary value problems is defined, and its relation with the hypoellipticity of certain pseudo-differential operators on the boundary is discussed (for second order equations). A theorem covering smoothness of solutions of boundary value problems such as $ a(x)\partial u/\partial n + b(x)u = f(x)$ for the Laplace equation is proved. An almost complete characterization of hypoelliptic boundary value problems for elliptic second order equations in two dimensions is given via analysis of hypoelliptic pseudo-differential operators in one variable.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0407436-4
Keywords: Boundary value problems, elliptic equations, hypoelliptic pseudo-differential operators, symbols, ordinary pseudo-differential operators
Article copyright: © Copyright 1976 American Mathematical Society

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