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Generalized Strichartz Inequalities for the Wave Equation

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Partial Differential Operators and Mathematical Physics

Part of the book series: Operator Theory Advances and Applications ((OT,volume 78))

Abstract

Strichartz inequalities for the wave equation □u = f are estimates of the solution u of the Cauchy problem for that equation, in the form of space time integral norms, in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data.

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References

  1. J. Bergh and J. Löfström, Interpolation spaces, Springer, Berlin, 1976.

    MATH  Google Scholar 

  2. P. Brenner, On L p-L p′, estimates for the wave equation, Math. Z., 145(1975), 251–254.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Ginibre, A. Soffer and G. Velo, The global Cauchy problem for the critical non linear wave-equation, J. Funct. Anal., 110(1992), 96–130.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Ginibre and G. Velo, Scattering theory in the energy space for a class of non-linear Schrödinger equations, J. Math. Pures Appl., 64(1984), 363–401.

    MathSciNet  Google Scholar 

  5. J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z., 189(1985), 487–505.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Ginibre and G. Velo, Conformal invariance and time decay for nonlinear wave equations, II, Ann. Inst. Henri Poincaré (Physique Théorique), 47(1987), 263–276.

    MathSciNet  Google Scholar 

  7. J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear wave equations, Commun. Math. Phys., 123(1989), 535–573.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Ginibre and G. Velo, Smoothing properties and retarded estimates for some dispersive evolution equations, Commun. Math. Phys., 144(1992), 163–188.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, Preprint Orsay 94–60, submitted to J. Func. Anal.

    Google Scholar 

  10. L. Kapitanski, Some generalisations of the Strichartz-Brenner inequality, Leningrad Math. J., 1(1990), 693–726.

    MathSciNet  Google Scholar 

  11. L. Kapitanski, Cauchy problem for a semilinear wave equation, II, Jour. Sov. Math. 62 (1992), 2746–2776. 111 ibid 2619–2645.

    Article  Google Scholar 

  12. T. Kato, Nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré (Physique Théorique), 46(1987), 113–129.

    MATH  Google Scholar 

  13. H. Lindblad and C. D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, preprint.

    Google Scholar 

  14. B. Marshall, Mixed norm estimates for the Klein-Gordon equation, inProc. Conf. Harm. Anal. in honor of A. Zygmund, Wadsworth, 1981, pp. 638–649.

    Google Scholar 

  15. G. Mockenhaupt, A. Seeger and C. D. Sogge, Local smoothing of Fourier integrals and Carleson-Sjölin estimates, J. Amer. Math. Soc., 6(1993), 65–130.

    MathSciNet  MATH  Google Scholar 

  16. H. Pecher, L p-Abschätzungen and klassische Lösungen für nichtlineare Wellengleichungen, I, Math. Z. 150(1976), 159–183.

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z., 185(1984), 261–270.

    Article  MathSciNet  MATH  Google Scholar 

  18. I. E. Segal, Space-time decay for solutions of wave equations, Adv. Math., 22(1976), 304–311.

    Article  Google Scholar 

  19. R. S. Strichartz, Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44(1977), 705–774.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Triebel, Theory of function spaces, Birkhäuser, Basel, 1983.

    Book  Google Scholar 

  21. K. Yajima, Existence of solutions for Schrodinger evolution equations, Commun. Math. Phys., 110(1987), 415–426.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Math. J., 39(1990), 229–248.

    Article  MathSciNet  MATH  Google Scholar 

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Ginibre, J., Velo, G. (1995). Generalized Strichartz Inequalities for the Wave Equation. In: Demuth, M., Schulze, BW. (eds) Partial Differential Operators and Mathematical Physics. Operator Theory Advances and Applications, vol 78. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9092-2_17

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  • DOI: https://doi.org/10.1007/978-3-0348-9092-2_17

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9903-1

  • Online ISBN: 978-3-0348-9092-2

  • eBook Packages: Springer Book Archive

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