@incollection{JEDP_1993____A15_0,
author = {Sogge, Christopher D.},
title = {$L^p$ estimates for the wave equation and applications},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {15},
pages = {1--12},
year = {1993},
publisher = {Ecole polytechnique},
doi = {10.5802/jedp.452},
mrnumber = {94f:35076},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jedp.452/}
}
TY - JOUR AU - Sogge, Christopher D. TI - $L^p$ estimates for the wave equation and applications JO - Journées équations aux dérivées partielles PY - 1993 SP - 1 EP - 12 PB - Ecole polytechnique UR - https://www.numdam.org/articles/10.5802/jedp.452/ DO - 10.5802/jedp.452 LA - en ID - JEDP_1993____A15_0 ER -
Sogge, Christopher D. $L^p$ estimates for the wave equation and applications. Journées équations aux dérivées partielles (1993), article no. 15, 12 p.. doi: 10.5802/jedp.452
1. , Lp boundedness of Fourier integrals, Mem. Amer. Math. Soc. 264 (1982). | Zbl
2. and , Low regularity local solutions for field equations, preprint. | Zbl
3. , Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69-85. | MR | Zbl
4. , Besicovitch type maximal operators and applications to Fourier analysis, Geometric and Funct. Anal. 1 (1991), 69-85. | MR | Zbl
5. , A harmonic analysis approach to problems in nonlinear differential equations, preprint. | Zbl
6. , Lectures on singular integral operators, C.B.M.S. Lecture Notes, no. 77, American Math. Soc., Providence, RI, 1990. | MR | Zbl
7. and , Dispersion of low-amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109. | MR | Zbl
8. , Lp bounds for eigenfunctions and spectral projections of the Laplacian near concave boundaries, Thesis, UCLA (1992).
9. , Regularity for the wave equation with a critical nonlinearity, Comm. Pure and Appl. Math. 45 (1992), 749-774. | MR | Zbl
10. , On Lebesgue space estimates for the wave equation, Indiana Math. J. 39 (1990), 229-248. | MR | Zbl
11. , The spectral function of an elliptic operator, Acta Math. 121 (1968), 193-218. | MR | Zbl
, Non-linear hyperbolic differential equations, Lund lecture notes, 1988.
13. , The ultrahyperbolic equation with 4 independent variables, Duke J. Math. 4 (1938), 300-322. | JFM | Zbl
14. , and , Decay estimates for Schrödinger operators, Comm. Pure and Appl. Math. 44 (1991), 573-604. | MR | Zbl
15. , Weak and yet weaker solutions of semilinear wave equations, Brown Univ. preprint. | Zbl
16. , and , Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), 329-349. | MR | Zbl
17. and , The null condition and global existence for nonlinear waves, Comm. Pure and Appl. Math. (to appear).
18. , A sharp counter example to local existence of low regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993) (to appear). | MR | Zbl
19. and , Minimal regularity for local existence of solutions to for semilinear Lorentz-invariant wave equations, in preparation.
20. , Lp → Lq estimates for singular integrals, Proc. Symp. Pure and Appl. Math., vol. 23, Amer. Math. Soc., 1973, pp. 479-481. | MR | Zbl
21. , and , Wave front sets, local smoothing and Bourgain's circular maximal theorem, Annals of Math. 136 (1992), 207-218. | MR | Zbl
22. , and , Local smoothing of Fourier integrals and Carleson-Sjölin estimates, J. Amer. Math. Soc. 6 (1993), 65-130. | MR | Zbl
23. , Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), 114-145. | MR | Zbl
24. , The u5-Klein-Gordan equation, Nonlinear PDE's and applications, vol. 53, Pitman Research Notes in Math., pp. 335-364. | MR | Zbl
25. and , Regularity results for nonlinear wave equations, preprint. | Zbl
26. , and , Regularity properties of Fourier integral operators, Annals of Math 134 (1991), 231-251. | MR | Zbl
27. and , Lp regularity for the wave equation with strictly convex obstacles (to appear). | Zbl
28. , Uniqueness in Cauchy problems for hyperbolic differential operators, Trans. Amer. Math. Soc. 333 (1992), 821-833. | MR | Zbl
29. , Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), 349-376. | MR | Zbl
30. , Fourier integrals in classical analysis, Cambridge Univ. Press, Cambridge, New York, 1993. | MR | Zbl
31. , Harmonic analysis real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, 1993. | MR | Zbl
32. , Nonlinear wave equations, C.B.M.S. Lecture Notes, no. 73, American Math. Soc., Providence, RI, 1989. | MR | Zbl
33. , A priori estimates for the wave equation and some applications, J. Funct. Analysis 5 (1970), 218-235. | MR | Zbl
34. , Restriction of Fourier transform to quadratic surfaces and decay of solutions to the wave equation, Duke Math. J. 44 (1977), 705-714. | MR | Zbl
35. , Semilinear wave equations, Bull. Amer. Math. Soc. 26 (1992), 53-85. | MR | Zbl
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