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

Bergamasco, Adalberto P.; Gerszonowicz, Jorge A.; Petronilho, Gerson

doi:10.1090/S0002-9947-1989-0929659-7

On the regularity up to the boundary in the Dirichlet problem for degenerate elliptic equations
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by Adalberto P. Bergamasco, Jorge A. Gerszonowicz and Gerson Petronilho PDF

Trans. Amer. Math. Soc. 313 (1989), 317-329 Request permission

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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Introduction to pseudo-differential and Fourier integral operators