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Propagation of singularities of solutions to semilinear boundary value problems


Authors: Florin David and Mark Williams
Journal: Bull. Amer. Math. Soc. 15 (1986), 201-204
MSC (1980): Primary 58G17, 35L70
DOI: https://doi.org/10.1090/S0273-0979-1986-15472-8
MathSciNet review: 854554
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  • 1. Ali Alabidi, Réflexion transverse des singularités pour un problème aux limites non linéaire d’ordre 2, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 10, 287–290 (French, with English summary). MR 786901
  • 2. Michael Beals, Propagation of smoothness for nonlinear second-order strictly hyperbolic differential equations, Pseudodifferential operators and applications (Notre Dame, Ind., 1984) Proc. Sympos. Pure Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 21–44. MR 812282, https://doi.org/10.1090/pspum/043/812282
  • 3. Michael Beals and Michael Reed, Propagation of singularities for hyperbolic pseudodifferential operators with nonsmooth coefficients, Comm. Pure Appl. Math. 35 (1982), no. 2, 169–184. MR 644021, https://doi.org/10.1002/cpa.3160350203
  • 4. F. David and M. Williams, Singularities of solutions to semilinear boundary value problems (in preparation).
  • 5. Lars Hörmander, Linear partial differential operators, Third revised printing. Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York Inc., New York, 1969. MR 0248435
  • 6. Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
    Lars Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985. Fourier integral operators. MR 781537
  • 7. Richard B. Melrose, Microlocal parametrices for diffractive boundary value problems, Duke Math. J. 42 (1975), no. 4, 605–635. MR 0517101
  • 8. R. B. Melrose and J. Sjöstrand, Singularities of boundary value problems. I, Comm. Pure Appl. Math. 31 (1978), no. 5, 593–617. MR 0492794, https://doi.org/10.1002/cpa.3160310504
  • 9. Jeffrey Rauch, Singularities of solutions to semilinear wave equations, J. Math. Pures Appl. (9) 58 (1979), no. 3, 299–308. MR 544255
  • 10. Monique Sablé-Tougeron, Paralineárisation de problèmes aux limites non linéaires, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 6, 169–171 (French, with English summary). MR 759224
  • 11. Monique Sablé-Tougeron, Régularité microlocale pour des problèmes aux limites non linéaires, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 10, 283–286 (French, with English summary). MR 786900, https://doi.org/10.5802/aif.1037
  • 12. Michael E. Taylor, Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure Appl. Math. 29 (1976), no. 1, 1–38. MR 0397175, https://doi.org/10.1002/cpa.3160290102

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DOI: https://doi.org/10.1090/S0273-0979-1986-15472-8