Well posedness in C ∞ for a weakly hyperbolic second order equation

Piero D'Ancona

Rendiconti del Seminario Matematico della Università di Padova (1994)

  • Volume: 91, page 65-83
  • ISSN: 0041-8994

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D'Ancona, Piero. "Well posedness in $C^\infty $ for a weakly hyperbolic second order equation." Rendiconti del Seminario Matematico della Università di Padova 91 (1994): 65-83. <http://eudml.org/doc/108328>.

@article{DAncona1994,
author = {D'Ancona, Piero},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Oleinik conditions; global well-posedness in },
language = {eng},
pages = {65-83},
publisher = {Seminario Matematico of the University of Padua},
title = {Well posedness in $C^\infty $ for a weakly hyperbolic second order equation},
url = {http://eudml.org/doc/108328},
volume = {91},
year = {1994},
}

TY - JOUR
AU - D'Ancona, Piero
TI - Well posedness in $C^\infty $ for a weakly hyperbolic second order equation
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1994
PB - Seminario Matematico of the University of Padua
VL - 91
SP - 65
EP - 83
LA - eng
KW - Oleinik conditions; global well-posedness in
UR - http://eudml.org/doc/108328
ER -

References

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  1. [CS] F. Colombini - S. Spagnolo, An example of a weakly hyperbolic Cauchy problem not well posed, Acta Math., 148 (1982), pp. 243-253. Zbl0517.35053MR666112
  2. [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. Zbl0706.35077MR966182
  3. [Fe] H. Federer, Geometric measure theory, Springer, Berlin (1969). Zbl0874.49001
  4. [Gi] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhaüser, Boston (1984). Zbl0545.49018MR775682
  5. [Ma] V. Maz'ja, Sobolev Spaces, Springer, Berlin (1985). MR817985
  6. [Ni1] T. Nishitani, The Cauchy problem for weakly hyperbolic equations of second order, Comm. PDEs, 5 (1980), pp. 1273-1296. Zbl0497.35053MR593968
  7. [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. Zbl0536.35042MR704720
  8. [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. Zbl0552.35049MR737827
  9. [O1] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 569-586. MR264227

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