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## Banach Center Publications

1997 | 41 | 1 | 91-108
Tytuł artykułu

### Fourier integral operators and nonlinear wave equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
91-108
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
• Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.
Bibliografia
• [1] J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69-85.
• [2] G. Eskin, Degenerate elliptic pseudo-differential operators of principal type (Russian), Mat. Sbornik 82 (124) (1970), 585-628; English translation, Math. USSR Sbornik 11 (1970), 539-582.
• [3] V. Georgiev, H. Lindblad and C. D. Sogge, Weighted Strichartz estimates and global existence for semilinear wave equations, Amer. J. Math., to appear.
• [4] R. Glassey, Finite-time blow-up for solutions of nonlinear wave equations Math. Z. 177, 323-340.
• [5] R. Glassey, Existence in the large for ☐u=F(u) in two dimensions, Math. Z 178 (1981), 233-261
• [6] J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Math. J. 39 (1990), 229-248.
• [7] L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), 79-183.
• [8] D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Annals of Math. 121 (1985), 463-494.
• [9] F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979), 235-265.
• [10] H. Kubo, On the critical decay and power for semilinear wave equations in odd space dimensions, preprint.
• [11] H. Lindblad and C. D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), 357-426.
• [12] H. Lindblad and C. D. Sogge, Long-time existence for small amplitude semilinear wave equations, Amer. J. Math. 118 (1996), 1047-1135.
• [13] H. Lindblad and C. D. Sogge, Restriction theorems and semilinear Klein-Gordon equations in (1+3)-dimensions, Duke Math. J. 85 (1996), 227-252.
• [14] C. Müller, On the behavior of the solutions of the differential equation ΔU=F(x,U) in the neighborhood of a point, Comm. Pure Appl. Math. 7 (1954), 505-514.
• [15] J. Schaeffer, The equation $u_{tt}-Δ u=|u|^p$ for the critical value of p, Proc. Royal Soc. Edinburgh 101 (1985), 31-44.
• [16] A. Seeger, C. D. Sogge and E. M. Stein, Regularity properties of Fourier integral operators, Annals of Math. 134 (1985), 231-251.
• [17] T. Sideris, Nonexistence of global solutions of wave equations in high dimensions, Comm. Partial Diff. Equations 12 (1987), 378-406.
• [18] C. D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349-376.
• [19] C. D. Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Math. 105, Cambridge Univ. Press, Cambridge, 1993.
• [20] C. D. Sogge, Lectures on nonlinear wave equations, International Press, Cambridge, 1995.
• [21] C. D. Sogge and E. M. Stein, Averages of functions over hypersurfaces: Smoothness of generalized Radon transforms, J. Analyse Math. 54, 165-188.
• [22] E. M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492.
• [23] W. Strauss, Nonlinear scattering theory, Scattering theory in mathematical physics, Reidel, Dordrect, 1979, pp. 53-79.
• [24] W. Strauss, Nonlinear scattering at low energy, J. Funct. Anal. 41 (1981), 110-133.
• [25] R. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Analysis 5 (1970), 218-235.
• [26] T. Wolff, A sharp $L^3$ estimate via incidence geometry, Amer. J. Math. (to appear).
• [27] Y. Zhou, Cauchy problem for semilinear wave equations with small data in four space dimensions, J. Diff. Equations 8 (1995), 135-144.
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Bibliografia
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