Bergamasco, Adalberto P.; Gerszonowicz, Jorge A.; Petronilho, Gerson On the regularity up to the boundary in the Dirichlet problem for degenerate elliptic equations. (English) Zbl 0681.35021 Trans. Am. Math. Soc. 313, No. 1, 317-329 (1989). Regularity up to the boundary of solutions to certain factorizable second order degenerate elliptic equations in the plane satisfying Dirichlet boundary conditions are derived. This follows from the regularity up to the boundary for some pseudodifferential equations, using parametrices of the Cauchy problem for the associated heat equation. Reviewer: M.Langlais Cited in 1 Document MSC: 35D10 Regularity of generalized solutions of PDE (MSC2000) 35J70 Degenerate elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35S99 Pseudodifferential operators and other generalizations of partial differential operators Keywords:associated heat equation PDFBibTeX XMLCite \textit{A. P. Bergamasco} et al., Trans. Am. Math. Soc. 313, No. 1, 317--329 (1989; Zbl 0681.35021) Full Text: DOI References: [1] Mohamed Salah Baouendi, Sur une classe d’opérateurs elliptiques dégénérés, Bull. Soc. Math. France 95 (1967), 45 – 87 (French). · Zbl 0179.19501 [2] V. V. Grusin and M. I. Visik, Boundary value problems for elliptic equations degenerate on the boundary of a domain, Math. USSR-Sb. 9 (1969), 423. [3] Lars Hörmander, Pseudo-differential operators and hypoelliptic equations, Singular integrals (Proc. Sympos. Pure Math., Vol. X, Chicago, Ill., 1966), Amer. Math. Soc., Providence, R.I., 1967, pp. 138 – 183. [4] J. Sjöstrand, Fourier integral operators with complex phase functions, Seminar on Singularities of Solutions of Linear Partial Differential Equations (Inst. Adv. Study, Princeton, N.J., 1977/78) Ann. of Math. Stud., vol. 91, Princeton Univ. Press, Princeton, N.J., 1979, pp. 51 – 64. [5] F. Treves, Solution of Cauchy problems modulo flat functions, Comm. Partial Differential Equations 1 (1976), no. 1, 45 – 72. [6] -, Boundary value problems for elliptic equations, Lecture notes, Bressanone, June 1977. [7] -, Introduction to pseudo-differential and Fourier integral operators (2 vols.), Plenum, New York, 1980. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.