Restriction theorems and semilinear Klein-Gordon equations in $(1+3)$-dimensions

previous :: next

Restriction theorems and semilinear Klein-Gordon equations in $(1+3)$-dimensions

Hans Lindblad and Christopher D. Sogge

Source: Duke Math. J. Volume 85, Number 1 (1996), 227-252.

First Page: Show

Primary Subjects: 35L70

Secondary Subjects: 35Q53

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243044
Mathematical Reviews number (MathSciNet): MR1412445
Zentralblatt MATH identifier: 0865.35077
Digital Object Identifier: doi:10.1215/S0012-7094-96-08510-5

back to Table of Contents

References

[1] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36.

Mathematical Reviews (MathSciNet): MR41:2468

Zentralblatt MATH: 0188.42601

Digital Object Identifier: doi:10.1007/BF02394567

[2] G. Georgiev and P. Popivanov, Global solution to the two-dimensional Klein-Gordon equation, Comm. Partial Differential Equations 16 (1991), no. 6-7, 941–995.

Mathematical Reviews (MathSciNet): MR92g:35140

Zentralblatt MATH: 0741.35039

Digital Object Identifier: doi:10.1080/03605309108820786

[3] L. Hörmander, The lifespan of classical solutions of nonlinear hyperbolic equations, Pseudodifferential operators (Oberwolfach, 1986), Lecture Notes in Math., vol. 1256, Springer, Berlin, 1987, pp. 214–280.

Mathematical Reviews (MathSciNet): MR88j:35024

Zentralblatt MATH: 0632.35045

[4] L. Hörmander, Nonlinear hyperbolic differential equations, Lund Univ. Lecture Notes, unpublished, 1988.

[5] L. Hörmander, On Sobolev spaces associated with some Lie algebras, Current topics in partial differential equations, Kinokuniya, Tokyo, 1986, pp. 261–287.

Mathematical Reviews (MathSciNet): MR1112150

Zentralblatt MATH: 0658.46023

[6] F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979), no. 1-3, 235–268.

Mathematical Reviews (MathSciNet): MR80i:35114

Zentralblatt MATH: 0406.35042

Digital Object Identifier: doi:10.1007/BF01647974

[7] S. Klainerman, Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, Comm. Pure Appl. Math. 38 (1985), no. 5, 631–641.

Mathematical Reviews (MathSciNet): MR87e:35080

Zentralblatt MATH: 0597.35100

Digital Object Identifier: doi:10.1002/cpa.3160380512

[8] S. Klainerman, Remark on the asymptotic behavior of the Klein-Gordon equation in $\bf R\sp n+1$, Comm. Pure Appl. Math. 46 (1993), no. 2, 137–144.

Mathematical Reviews (MathSciNet): MR93k:35046

Zentralblatt MATH: 0805.35104

Digital Object Identifier: doi:10.1002/cpa.3160460202

[9] R. Kosecki, The unit condition and global existence for a class of nonlinear Klein-Gordon equations, J. Differential Equations 100 (1992), no. 2, 257–268.

Mathematical Reviews (MathSciNet): MR93k:35178

Zentralblatt MATH: 0781.35062

Digital Object Identifier: doi:10.1016/0022-0396(92)90114-3

[10] H. Lindblad, Blow-up for solutions of $\square u=\vert u\vert \sp p$ with small initial data, Comm. Partial Differential Equations 15 (1990), no. 6, 757–821.

Mathematical Reviews (MathSciNet): MR91k:35168

Zentralblatt MATH: 0712.35018

Digital Object Identifier: doi:10.1080/03605309908820708

[11] H. Lindblad and C. D. Sogge, Long-time existence for small amplitude semilinear wave equations, to appear in Amer. J. Math.

Mathematical Reviews (MathSciNet): MR1408499

Zentralblatt MATH: 0869.35064

Digital Object Identifier: doi:10.1353/ajm.1996.0042

[12] J. L. Rubio de Francia, Transference principles for radial multipliers, Duke Math. J. 58 (1989), no. 1, 1–19.

Mathematical Reviews (MathSciNet): MR90m:42023

Zentralblatt MATH: 0676.42009

Digital Object Identifier: doi:10.1215/S0012-7094-89-05801-8

Project Euclid: euclid.dmj/1077307369

[13] I. Segal, Space-time decay for solutions of wave equations, Advances in Math. 22 (1976), no. 3, 305–311.

Mathematical Reviews (MathSciNet): MR58:11945

Zentralblatt MATH: 0344.35058

Digital Object Identifier: doi:10.1016/0001-8708(76)90097-9

[14] J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math. 38 (1985), no. 5, 685–696.

Mathematical Reviews (MathSciNet): MR87b:35160

Zentralblatt MATH: 0597.35101

Digital Object Identifier: doi:10.1002/cpa.3160380516

[15] C. D. Sogge, Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, vol. 105, Cambridge University Press, Cambridge, 1993.

Mathematical Reviews (MathSciNet): MR94c:35178

Zentralblatt MATH: 0783.35001

[16] C. D. Sogge, Lectures on nonlinear wave equations, Monographs in Analysis, II, International Press, Boston, MA, 1995.

Mathematical Reviews (MathSciNet): MR2000g:35153

[17] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.

Mathematical Reviews (MathSciNet): MR44:7280

Zentralblatt MATH: 0207.13501

[18] R. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), no. 3, 705–714.

Mathematical Reviews (MathSciNet): MR58:23577

Zentralblatt MATH: 0372.35001

Digital Object Identifier: doi:10.1215/S0012-7094-77-04430-1

Project Euclid: euclid.dmj/1077312392

[19] P. Tomas, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477–478.

Mathematical Reviews (MathSciNet): MR50:10681

Zentralblatt MATH: 0298.42011

Digital Object Identifier: doi:10.1090/S0002-9904-1975-13790-6

Project Euclid: euclid.bams/1183536437

[20] L. Vega, Restriction theorems and the Schrödinger multiplier on the torus, Partial differential equations with minimal smoothness and applications (Chicago, IL, 1990), IMA Vol. Math. Appl., vol. 42, Springer, New York, 1992, pp. 199–211.

Mathematical Reviews (MathSciNet): MR93e:42025

Zentralblatt MATH: 0791.42011

[21] N. J. Vilenkin, Special functions and the theory of group representations, Translated from the Russian by V. N. Singh. Translations of Mathematical Monographs, Vol. 22, American Mathematical Society, Providence, R. I., 1968.

Mathematical Reviews (MathSciNet): MR37:5429

Zentralblatt MATH: 0172.18404

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?