This is a preview of subscription content, log in via an institution to check access.
References
Bergh, J., Löfström, J.: Interpolation spaces. Berlin-Heidelberg-New York: Springer 1976
Brenner, P.: OnL p-Lp ′, estimates for the wave equation. Math. Z.145, 251–254 (1975)
Brenner, P.: On the existence of global smooth solutions of certain semilinear hyperbolic equations. Math. Z.167, 99–135 (1979)
Brenner, P., von, Wahl, W.: Global classical solutions of non-linear wave equations. Math. Z.176, 87–121 (1981)
Browder, F.E.: On nonlinear wave equations. Math. Z.80, 249–264 (1962)
Ginibre, J., Velo, G.: The global Cauchy problem for the nonlinear Schrödinger equation revisited. Ann. Inst. Henri Poincaré (in press)
Glassey, R., Tsutsumi, M.: On uniqueness of weak solutions to semi linear wave equations. Commun. Partial Differ. Equations7, 153–195 (1982)
Heinz, E., von Wahl, W.: Zu einem Satz von F.E. Browder über nichtlineare Wellengleichungen. Math. Z.141, 33–45 (1975)
Hörmander, L.: The analysis of linear partial differential operators. I.. Berlin-Heidelberg-New York: Springer 1983
Jörgens, K.: Das Anfangswertproblem im Grossen für eine Klasse nichtlinearer Wellengleichungen. Math. Z.77, 295–308 (1961)
Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod and Gauthier-Villars 1969
Parenti, C., Strocchi, F., Velo, G.: A local approach to some nonlinear evolution equations of hyperbolic type. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.3, 443–500 (1976)
Pecher, H.:L p-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen I. Math. Z.150, 159–183 (1976)
Pecher, H.: Ein nichtlinearer Interpolationssatz und seine Anwendung auf nichtlineare Wellengleichungen. Math. Z.161, 9–40 (1978)
Pecher, H.: Nonlinear small data scattering for the wave and Klein-Gordon equation. Math. Z.185, 261–270 (1984)
Pecher, H.: Low energy scattering for nonlinear Klein-Gordon equations., Preprint
Peral, J.C.:L p-estimates for the wave equations J. Funct. Anal.36, 114–145 (1980)
Reed, M.: Abstract nonlinear wave equations Berlin-Heidelberg-New York: Springer 1976
Segal, I.E.: The global Cauchy Problem for a relativistic scalar field with power interaction. Bull. Soc. Math. Fr.91, 129–135 (1963)
Segal, I.E.: Nonlinear semigroups. Ann. Math.78, 339–364 (1963)
Segal, I.E.: Space-time decay for solutions of wave equations., Adv. Math.22, 305–311 (1976)
Strauss, W.: Decay and asymptotics for □u=f(u). J. Funct. Anal.2, 409–457 (1968)
Strauss, W.: On weak solutions of semilinear hyperbolic equations. An. Acad. Bras. Cienc.42, 645–651 (1970)
Strauss, W.: Nonlinear scattering theory at low energy. J. Funct. Anal.41, 110–133 (1981). Ibid. Strauss, W.: Nonlinear scattering theory at low energy. J. Funct. Anal.43, 281–293 (1981)
Strichartz, R.: Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J.44, 705–714 (1977)
Triebel, H.: Spaces of distributions of Besov type on Euclideann-space. Duality, interpolation. Ark. Mat.11, 13–64 (1973)
Triebel, H.: Theory of function spaces. Basel: Birkhäuser 1983
von Wahl, W.: Klassische Lösungen nichtlinearer Wellengleichungen im Grossen. Math. Z.112, 241–279 (1969)
von Wahl, W.: Über nichtlineare Wellengleichungen mit zeitabhängigem elliptischem Hauptteil. Math. Z.142, 105–120 (1975)
Author information
Authors and Affiliations
Additional information
Laboratoire associé Centre National de la Recherche Scientifique
Rights and permissions
About this article
Cite this article
Ginibre, J., Velo, G. The global Cauchy problem for the non linear Klein-Gordon equation. Math Z 189, 487–505 (1985). https://doi.org/10.1007/BF01168155
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01168155