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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the regularity up to the boundary in the Dirichlet problem for degenerate elliptic equations


Authors: Adalberto P. Bergamasco, Jorge A. Gerszonowicz and Gerson Petronilho
Journal: Trans. Amer. Math. Soc. 313 (1989), 317-329
MSC: Primary 35J70; Secondary 35B65, 35S15
MathSciNet review: 929659
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Abstract: We give a simple proof of the regularity up to the boundary of solutions of the Dirichlet problem for a class of second-order degenerate elliptic equations in the plane. We show that the method of transfer to the boundary via the associated heat equations, can be used to reduce the problem to proving the ellipticity or hypoellipticity of a pseudodifferential operator on the boundary.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0929659-7
PII: S 0002-9947(1989)0929659-7
Article copyright: © Copyright 1989 American Mathematical Society