On the regularity of the variational solution of the Tricomi problem in the elliptic region
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 19 (1985) no. 2, p. 327-340
@article{M2AN_1985__19_2_327_0,
     author = {Vanninathan, M. and Veerappa Gowda, G. D.},
     title = {On the regularity of the variational solution of the Tricomi problem in the elliptic region},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {19},
     number = {2},
     year = {1985},
     pages = {327-340},
     zbl = {0573.35067},
     mrnumber = {802598},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1985__19_2_327_0}
}
Vanninathan, M.; Veerappa Gowda, G. D. On the regularity of the variational solution of the Tricomi problem in the elliptic region. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 19 (1985) no. 2, pp. 327-340. http://www.numdam.org/item/M2AN_1985__19_2_327_0/

[1] M. Abramowitz and A. Stegun, Handbook of Mathematical Functions, Dover Publications Inc., New York, 1970.

[2] L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, John Wiley, New York, 1958. | MR 96477 | Zbl 0083.20501

[3] A. V. Bitsadze, Equations of the Mixed Type, Macmillan, New York, 1964. | MR 163078 | Zbl 0111.29205

[4] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. | MR 520174 | Zbl 0383.65058

[5] A. G. Deacon and S. Osher, A Finite Element Method for a boundary value problem of mixed type, SIAM J. Numer. Anal., 16 (5) (1979), pp. 756-778. | MR 543966 | Zbl 0438.65093

[6] C. Ferrari and F. G. Tricomi, Transonic Aerodynamics, Academic Press, New York, 1968. | Zbl 0177.55304

[7] P. Germain, Bader, Solutions Elémentaires de certaines Equations aux dérivées partielles du type mixte, Bull. Soc. Math. Fr. 81 (1953), pp. 145-174. | Numdam | MR 58834 | Zbl 0051.07503

[8] P. Grisvard, Behaviour of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, Numerical solutions of Partial Differential Equations III. Synspade 1975, Bert Hubbord Ed., pp. 207-274. | MR 466912 | Zbl 0361.35022

[9] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, New York, 1966. | MR 203473 | Zbl 0148.12601

[10] V. A. Kondratev, Boundary problems for Elliptic Equations in Domains with conical or Angular points, Trans. Moscow. Math. Soc., Trudy, Vol. 16 (1967), (Russian), pp. 209-292. AMS Translations, 1968. | MR 226187 | Zbl 0194.13405

[11] C. Morawetz, A uniqueness theorem for Frankl's problem, Comm. Pure Appl. Math., 7 (1954), pp. 697-703. | MR 65791 | Zbl 0056.31904

[12] C. Morawetz, A weak solution for a system of equations of elliptic-hyperbolic type, Comm. Pure Appl. Math., 11 (1958), pp. 315-331. | MR 96893 | Zbl 0081.31201

[13] C. Morawetz, Uniqueness for the analogue of the Neumann problem for Mixed Equations, The Michigan Math. J., 4 (1957), pp. 5-14. | MR 85441 | Zbl 0077.09602

[14] S. Nocilla, G. Geymonat; B. Gabotti, Il profil alose ad arco di cerchio in flusso transonico continuo senzi incidenza, Annali di Mat. Pura ed applicat, 84 (1970), pp. 341-374. | Zbl 0233.76126

[15] S. Osher, Boundary value problems for Equations of Mixed Type I, The Lavrentiev-Bitsadze Model, Comm. PDE, 2 (5) (1977), pp. 499-547. | MR 492931 | Zbl 0358.35055

[16] V. Pashkoviskii, A functional method of solving Tricomi Problem, Differencial'nye Uravneniya, 4 (1968), pp. 63-73 (Russian). | MR 235297 | Zbl 0233.35068

[17] B. Spain and M. G. Smith, Functions of Mathematical Physics, van Nostrand, London, 1970. | Zbl 0186.37501

[18] G. Strang and G. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N. J., 1973. | MR 443377 | Zbl 0356.65096

[19] J. A. Trangenstein, A Finite Element Method for the Tricomi Problem in the elliptic region, SIAM J. Numer. Anal., 14 (1977), pp. 1066-1077. | MR 471379 | Zbl 0399.65079

[20] J. A. Trangenstein, A Finite Element Method for the Tricomi Problem in the Elliptic Region, Thesis, Cornell University, Ithaca, N. Y. 1975.

[21] F. Treves, Introduction to Pseudo-Differential Operators and Fourier Integral Operators, Vol. I, Plenum Press, NewYork, 1980. | Zbl 0453.47027

[22] S Uspenskii, Imbedding and Extension theorems for a class of functions, II, Sib. Math. J., 7 (1966), pp. 409-418 (Russian). | MR 198223

[23] M. Vanninathan and G. D. Veerappa Gowda, Approximation of Tricomi. Problem with Neumann Boundary Condition, To appear. | MR 757493 | Zbl 0527.65077