Hypoellipticity of certain degenerate elliptic boundary value problems
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- by Yakar Kannai PDF
- Trans. Amer. Math. Soc. 217 (1976), 311-328 Request permission
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.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- 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