Well posedness in ${C}^{\infty }$ for a weakly hyperbolic second order equation
Rendiconti del Seminario Matematico della Università di Padova, Volume 91 (1994), p. 65-83
@article{RSMUP_1994__91__65_0,
author = {d'Ancona, Piero},
title = {Well posedness in $C^\infty$ for a weakly hyperbolic second order equation},
journal = {Rendiconti del Seminario Matematico della Universit\a di Padova},
publisher = {Seminario Matematico of the University of Padua},
volume = {91},
year = {1994},
pages = {65-83},
zbl = {0820.35097},
language = {en},
url = {http://www.numdam.org/item/RSMUP_1994__91__65_0}
}

D'Ancona, Piero. Well posedness in $C^\infty$ for a weakly hyperbolic second order equation. Rendiconti del Seminario Matematico della Università di Padova, Volume 91 (1994) pp. 65-83. http://www.numdam.org/item/RSMUP_1994__91__65_0/`

[CS] F. Colombini - S. Spagnolo, An example of a weakly hyperbolic Cauchy problem not well posed, Acta Math., 148 (1982), pp. 243-253. | MR 666112 | Zbl 0517.35053

[D] P. D'Ancona, Gevrey well posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. RIMS Kyoto Univ., 24 (1988), pp. 433-449. | MR 966182 | Zbl 0706.35077

[Fe] H. Federer, Geometric measure theory, Springer, Berlin (1969). | Zbl 0874.49001

[Gi] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhaüser, Boston (1984). | MR 775682 | Zbl 0545.49018

[Ma] V. Maz'Ja, Sobolev Spaces, Springer, Berlin (1985). | MR 817985

[Ni1] T. Nishitani, The Cauchy problem for weakly hyperbolic equations of second order, Comm. PDEs, 5 (1980), pp. 1273-1296. | MR 593968 | Zbl 0497.35053

[Ni2] T. Nishitani, Sur les équations hyperboliques à coefficients qui sont hölderiens en t et de classe de Gevrey en x, Sci. Math., 2e série, 107 (1983), pp. 113-138. | MR 704720 | Zbl 0536.35042

[Ni3] T. Nishitani, A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables, J. Math. Kyoto Univ., 24 (1984), pp. 91-104. | MR 737827 | Zbl 0552.35049

[O1] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 569-586. | MR 264227