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Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 338-418. [9] P. ”, Chelsea Publishing Co. New York, 1986. [10] N. Garofalo and E. Lanconelli, Existence and nonexistence results for semilinear equations on the Heisenberg group, Indiana Univ. Math. J. 41 (1992), 71-98. [11] S. Gellerstedt, Sur un probl`eme aux limites pour une ´equation lin´eaire aux d´eriv´ees partielles du second ordre de type mixtes, Dissertation, Uppsala University, Uppsala 1935.

43 [12] V. V. Grushin, Singularities of solutions to certain pseudodifferential and degenerating elliptic equations, Uspehi Mat. Nauk 26 (1971), 221-222. [13] P. Germain and R. Bader, Sur quelques probl`emes relatifs `a l’´equation de type mixte de Tricomi, O. N. E. R. A. Publ. 54 (1952). [14] M. Grillakis, Regularity of the wave equation with a critical nonlinearity, Comm. Pure Appl. Math. 45 (1992), 749-774. [15] S. Hawking and R. Penrose, “The nature of space and time”, The Issac Newton Institute Series of Lectures, Princeton University Press, Princeton, NJ, 1996.

36 of [24]), and so the rest of the proof amounts to a sequence of lengthy calculations which we will briefly summarize. 20) is given by N pr(2) v = v + ϕxj j=1 ∂ ∂ + ϕy + ∂uxj ∂uy N ϕxj xk j,k=1 ∂ ∂uxj xk N ϕxj y + j=1 ∂ ∂ + ϕyy ∂uxj y ∂uyy where the coefficients ϕxj , ϕy , etc. are calculated via a general formula and the expressions uxj , uy , etc. represent the coordinates in the higher order jet spaces. 19) depends only on y, uxj xj , uyy . 21) yields a polynomial in 1, u, Du, D2 u with coefficients that 39 depend on ξ, η, ϕ and their partial derivatives up to order two.