Petrovsky lacuna

Petrovsky lacunas are similar to the spaces between shock waves of a supersonic object.

In mathematics, a Petrovsky lacuna, named for the Russian mathematician I. G. Petrovsky, is a region where the fundamental solution of a linear hyperbolic partial differential equation vanishes. They were studied by (Petrovsky 1945) who found topological conditions for their existence.

Petrovsky's work was generalized and updated by Atiyah, Bott, and Gårding (1970, 1973).

References

• Atiyah, Michael Francis (1966–1968), "Hyperbolic differential equations and algebraic geometry (after Petrowsky)", Séminaire Bourbaki, Vol. 10, Paris: Société Mathématique de France, pp. 87–99, http://www.numdam.org/item?id=SB_1966-1968__10__87_0 .
• Atiyah, Michael Francis; Bott, Raoul; Gårding, Lars (1970), "Lacunas for hyperbolic differential operators with constant coefficients. I", Acta Mathematica 124: 109–189, doi:10.1007/BF02394570 .
• Atiyah, Michael Francis; Bott, Raoul; Gårding, Lars (1973), "Lacunas for hyperbolic differential operators with constant coefficients. II", Acta Mathematica 131: 145–206, doi:10.1007/BF02392039 .
• Petrovsky, I.G. (1945), "On the diffusion of waves and the lacunas for hyperbolic equations", Recueil Mathématique (Matematicheskii Sbornik) 17 (59) (3): 289–368, http://mi.mathnet.ru/eng/msb/v59/i3/p289 .