previous :: next
Local regularity of solutions to wave equations with time-dependent potentials
Alberto Ruiz and Luis Vega
Source: Duke Math. J. Volume 76, Number 3
(1994), 913-940.
First Page:
Show
Hide
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/1077287210
Mathematical Reviews number (MathSciNet): MR1309336
Zentralblatt MATH identifier: 0826.35014
Digital Object Identifier: doi:10.1215/S0012-7094-94-07636-9
References
[AH] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. Analyse Math. 30 (1976), 1–38.
Mathematical Reviews (MathSciNet): MR57:6776
Zentralblatt MATH: 0335.35013
Digital Object Identifier: doi:10.1007/BF02786703
[BAK] M. Ben-Arzi and S. Klainerman, Regularity and decay of evolution equations, to appear in J. Analyse Math.
[ChaS] S. Chanillo and E. Sawyer, Unique continuation for $\Delta+v$ and the C. Fefferman-Phong class, Trans. Amer. Math. Soc. 318 (1990), no. 1, 275–300.
Mathematical Reviews (MathSciNet): MR90f:35050
Zentralblatt MATH: 0702.35034
Digital Object Identifier: doi:10.2307/2001239
JSTOR: links.jstor.org
[ChiF] F. Chiarenza and M. Frasca, A remark on a paper by C. Fefferman: “The uncertainty principle”, Proc. Amer. Math. Soc. 108 (1990), no. 2, 407–409.
Mathematical Reviews (MathSciNet): MR91a:46030
Zentralblatt MATH: 0694.46029
Digital Object Identifier: doi:10.2307/2048289
JSTOR: links.jstor.org
[ChiR] F. Chiarenza and A. Ruiz, Uniform $L\sp 2$-weighted Sobolev inequalities, Proc. Amer. Math. Soc. 112 (1991), no. 1, 53–64.
Mathematical Reviews (MathSciNet): MR91h:46057
Zentralblatt MATH: 0745.35007
Digital Object Identifier: doi:10.2307/2048479
[CS1] P. Constantin and J. C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), no. 2, 413–439.
Mathematical Reviews (MathSciNet): MR89d:35150
Zentralblatt MATH: 0667.35061
Digital Object Identifier: doi:10.2307/1990923
JSTOR: links.jstor.org
[CS2] P. Constantin and J.-C. Saut, Local smoothing properties of Schrödinger equations, Indiana Univ. Math. J. 38 (1989), no. 3, 791–810.
Mathematical Reviews (MathSciNet): MR91e:35167
Zentralblatt MATH: 0712.35022
Digital Object Identifier: doi:10.1512/iumj.1989.38.38037
[Fe] C. Fefferman, A note on spherical summation multiliers, Israel J. Math. 14 (1973), 413–417.
Zentralblatt MATH: 0262.42007
Mathematical Reviews (MathSciNet): MR320624
Digital Object Identifier: doi:10.1007/BF02771772
[FeP] C. Fefferman and D. H. Phong, Lower bounds for Schrödinger equations, Conference on Partial Differential Equations (Saint Jean de Monts, 1982), Soc. Math. France, Paris, 1982, Conf. No. 7, 7.
Mathematical Reviews (MathSciNet): MR84a:35218
Zentralblatt MATH: 0492.35057
[H] J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Univ. Math. J. 39 (1990), no. 1, 229–248.
Mathematical Reviews (MathSciNet): MR91j:35158
Zentralblatt MATH: 0683.35008
Digital Object Identifier: doi:10.1512/iumj.1990.39.39013
[JoSoSg] J.-L. Journé, A. Soffer, and C. D. Sogge, $L\sp p\to L\sp p'$ estimates for time-dependent Schrödinger operators, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 519–524.
Mathematical Reviews (MathSciNet): MR91g:35080
Zentralblatt MATH: 0751.35011
Digital Object Identifier: doi:10.1090/S0273-0979-1990-15967-1
Project Euclid: euclid.bams/1183555906
[Ka] T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Studies in applied mathematics, Adv. Math. Suppl. Stud., vol. 8, Academic Press, New York, 1983, pp. 93–128.
Mathematical Reviews (MathSciNet): MR86f:35160
Zentralblatt MATH: 0549.34001
[KaY] T. Kato and K. Yajima, Some examples of smooth operators and the associated smoothing effect, Rev. Math. Phys. 1 (1989), no. 4, 481–496.
Mathematical Reviews (MathSciNet): MR91i:47013
Zentralblatt MATH: 0833.47005
Digital Object Identifier: doi:10.1142/S0129055X89000171
[KRS] C. E. Kenig, A. Ruiz, and C. D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), no. 2, 329–347.
Mathematical Reviews (MathSciNet): MR88d:35037
Zentralblatt MATH: 0644.35012
Digital Object Identifier: doi:10.1215/S0012-7094-87-05518-9
Project Euclid: euclid.dmj/1077306024
[KPV1] C. E. Kenig, G. Ponce, and L. Vega, Small solutions to nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), no. 3, 255–288.
Mathematical Reviews (MathSciNet): MR94h:35238
Zentralblatt MATH: 0786.35121
[KPV2] C. E. Kenig, G. Ponce, and L. Vega, On the Zakharov and Zakharov-Schulman systems, to appear in J. Funct. Anal.
Mathematical Reviews (MathSciNet): MR1308623
Zentralblatt MATH: 0823.35158
Digital Object Identifier: doi:10.1006/jfan.1995.1009
[KrF] S. N. Kruzhkov and A. V. Faminskii, Generalized solutions of the Cauchy problem for the $KdV$ equation, Math. USSR-Sb 48 (1984), 93–138.
[LSg] H. Lindblad and C. D. Sogge, Minimal regularity for local existence of solutions for semilinear Lorentz-invariant wave equations, preprint.
[P] J. Peetre, On the theory of $\cal L\sbp,\,\sb\lambda $ spaces, J. Functional Analysis 4 (1969), 71–87.
Mathematical Reviews (MathSciNet): MR39:3300
Zentralblatt MATH: 0175.42602
Digital Object Identifier: doi:10.1016/0022-1236(69)90022-6
[RS] M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1975.
Mathematical Reviews (MathSciNet): MR58:12429b
Zentralblatt MATH: 0308.47002
[RV] A. Ruiz and L. Vega, On local regularity of Schrödinger equations, Internat. Math. Res. Notices (1993), no. 1, 13–27.
Mathematical Reviews (MathSciNet): MR94c:35060
Zentralblatt MATH: 0812.35016
Digital Object Identifier: doi:10.1155/S1073792893000029
[SSj] P. Sjögren and P. Sjölin, Convergence properties for the time dependent Schrödinger equation, to appear in Ann. Acad. Sci. Fenn. Ser. A I Math.
Mathematical Reviews (MathSciNet): MR997967
[Sj] P. Sjölin, Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), no. 3, 699–715.
Mathematical Reviews (MathSciNet): MR88j:35026
Zentralblatt MATH: 0631.42010
Digital Object Identifier: doi:10.1215/S0012-7094-87-05535-9
Project Euclid: euclid.dmj/1077306171
[Ste] E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993.
Mathematical Reviews (MathSciNet): MR95c:42002
Zentralblatt MATH: 0821.42001
[Str] R. S. 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
[T] P. A. 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
[V1] L. Vega, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988), no. 4, 874–878.
Mathematical Reviews (MathSciNet): MR89d:35046
Zentralblatt MATH: 0654.42014
Digital Object Identifier: doi:10.2307/2047326
JSTOR: links.jstor.org
[V2] L. Vega, El multiplicador de Schrödinger: la función maximal $y$ los operadores de restricción, Ph.D. thesis, Universidad Autónoma de Madrid, 1988.
previous :: next
Duke Mathematical Journal
