Fourier integral operators and nonlinear wave equations
Banach Center Publications (1997)
- Volume: 41, Issue: 1, page 91-108
- ISSN: 0137-6934
Access Full Article
topHow to cite
topSogge, Christopher. "Fourier integral operators and nonlinear wave equations." Banach Center Publications 41.1 (1997): 91-108. <http://eudml.org/doc/252210>.
@article{Sogge1997,
author = {Sogge, Christopher},
journal = {Banach Center Publications},
keywords = {global existence theorem; D'Alembertian; inequality of Stricharz; inhomogeneous wave equation},
language = {eng},
number = {1},
pages = {91-108},
title = {Fourier integral operators and nonlinear wave equations},
url = {http://eudml.org/doc/252210},
volume = {41},
year = {1997},
}
TY - JOUR
AU - Sogge, Christopher
TI - Fourier integral operators and nonlinear wave equations
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 1
SP - 91
EP - 108
LA - eng
KW - global existence theorem; D'Alembertian; inequality of Stricharz; inhomogeneous wave equation
UR - http://eudml.org/doc/252210
ER -
References
top- [1] J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69-85. Zbl0626.42012
- [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. Zbl0893.35075
- [4] R. Glassey, Finite-time blow-up for solutions of nonlinear wave equations Math. Z. 177, 323-340. Zbl0438.35045
- [5] R. Glassey, Existence in the large for ☐u=F(u) in two dimensions, Math. Z 178 (1981), 233-261 Zbl0451.35039
- [6] J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Math. J. 39 (1990), 229-248. Zbl0683.35008
- [7] L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), 79-183. Zbl0212.46601
- [8] D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Annals of Math. 121 (1985), 463-494. Zbl0593.35119
- [9] F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979), 235-265. Zbl0406.35042
- [10] H. Kubo, On the critical decay and power for semilinear wave equations in odd space dimensions, preprint. Zbl0948.35082
- [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. Zbl0846.35085
- [12] H. Lindblad and C. D. Sogge, Long-time existence for small amplitude semilinear wave equations, Amer. J. Math. 118 (1996), 1047-1135. Zbl0869.35064
- [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. Zbl0865.35077
- [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 for the critical value of p, Proc. Royal Soc. Edinburgh 101 (1985), 31-44. Zbl0592.35080
- [16] A. Seeger, C. D. Sogge and E. M. Stein, Regularity properties of Fourier integral operators, Annals of Math. 134 (1985), 231-251. Zbl0754.58037
- [17] T. Sideris, Nonexistence of global solutions of wave equations in high dimensions, Comm. Partial Diff. Equations 12 (1987), 378-406. Zbl0555.35091
- [18] C. D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349-376. Zbl0754.35004
- [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. Zbl0695.42012
- [22] E. M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492. Zbl0072.32402
- [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. Zbl0466.47006
- [25] R. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Analysis 5 (1970), 218-235. Zbl0189.40701
- [26] T. Wolff, A sharp 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. Zbl0836.35099
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.