Well posedness under Levi conditions for a degenerate second order Cauchy problem
Ascanelli, Alessia
Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007), p. 113-126 / Harvested from Numdam
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@article{RSMUP_2007__117__113_0,
     author = {Ascanelli, Alessia},
     title = {Well posedness under Levi conditions for a degenerate second order Cauchy problem},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {117},
     year = {2007},
     pages = {113-126},
     mrnumber = {2351788},
     zbl = {1146.35054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2007__117__113_0}
}

Ascanelli, Alessia. Well posedness under Levi conditions for a degenerate second order Cauchy problem. Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007) pp. 113-126. http://gdmltest.u-ga.fr/item/RSMUP_2007__117__113_0/

[1] A. Ascanelli - M. Cicognani, Energy estimate and Fundamental Solution for Degenerate Hyperbolic Cauchy problems. J. Differential Equations, 217 (2005), pp. 305-340. | MR 2168825 | Zbl 1087.35066

[2] A. Ascanelli - M. Cicognani, Well posedness of the Cauchy problem for some degenerate hyperbolic operators. Pseudo-Differential Operators and Related Topics, Series: Operator Theory: Advances and Applications, Vol. 164, Editors: P. Boggiatto, L. Rodino, J. Toft, M.-W. Wong, Birkhuser Verlag Basel/Switzerland (2006), pp. 23-41. | MR 2243964 | Zbl 1101.35058

[3] M. D. Bronsïteǐn, The Cauchy problem for hyperbolic operators with characteristics of variable multiplicity. Trudy Moskov. Mat. Obshch. 41 (1980), pp. 83-99. | MR 611140 | Zbl 0468.35062

[4] M. Cicognani, The Cauchy problem for strictly hyperbolic operators with non-absolutely continuous coefficients. Tsukuba J. Math. 27 (2003), pp. 1-12. | MR 1999231 | Zbl 1041.35049

[5] M. Cicognani, Coefficients with unbounded derivatives in hyperbolic equations. Math. Nachr. 277 (2004), pp. 1-16. | MR 2100045 | Zbl 1060.35071

[6] F. Colombini - E. De Giorgi - S. Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps. Ann. Sc. Norm. Sup. Pisa 6 (1979), pp. 511-559. | Numdam | MR 553796 | Zbl 0417.35049

[7] F. Colombini - D. Del Santo - T. Kinoshita, Well posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (2002), pp. 327-358. | Numdam | MR 1991143 | Zbl 1098.35094

[8] F. Colombini - D. Del Santo - M. Reissig, On the optimal regularity coefficients in hyperbolic Cauchy problem, Bull. Sci. Math. 127 (2003), pp. 328-347. | MR 1988632 | Zbl 1037.35038

[9] F. Colombini - H. Ishida - N. Orru, On the Cauchy problem for finitely degenerate hyperbolic equations of second order. Ark. Mat. 38 (2000), pp. 223-230. | MR 1785400 | Zbl 1073.35145

[10] F. Colombini - E. Jannelli - S. Spagnolo, Well posedness in Gevrey classes of the Cauchy problem for a non strictly hyperbolic equation with coefficients depending on time. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (1983), pp. 291-312. | Numdam | MR 728438 | Zbl 0543.35056

[11] F. Colombini - T. Nishitani, On finitely degenerate hyperbolic operators of second order. Osaka J. Math. 41, 4 (2004) pp. 933-947. | MR 2116346 | Zbl 1068.35078

[12] V. Ja Ivriǐ, Conditions for correctness in Gevrey classes of the Cauchy problem for hyperbolic operators with characteristics of variable multiplicity. (Russian) Sibirsk. Mat. ZÏ. 17 (1976), pp. 1256-1270. | MR 454368 | Zbl 0352.35060

[13] K. Kajitani, Cauchy problem for nonstrictly hyperbolic systems in Gevrey classes. J. Math. Kyoto Univ. 23-3 (1983), pp. 599-616. | MR 721386 | Zbl 0544.35063

[14] A. Kubo - M. Reissig, Construction of parametrix for hyperbolic equations with fast oscillations in non-Lipschitz coefficients. Comm. Partial Differential Equations 28 (2003), pp. 1471-1502. | MR 1998944 | Zbl 1036.35118

[15] S. Mizohata, On the Cauchy problem. Notes and Reports in Mathematics in Science and Engineering, 3. Academic Press, Inc., Orlando, FL; Science Press, Beijing, 1985. | MR 860041 | Zbl 0616.35002

[16] T. Nishitani, The Cauchy problem for weakly hyperbolic equations of second order. Comm. Partial Differential Equations, 5 (1980), pp. 1273-1296. | MR 593968 | Zbl 0497.35053