Petrovsky lacuna

Petrovsky lacuna

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 harvtxt|Petrovsky|1945 who found topological conditions for their existence.

Petrovsky's work was generalized and updated by harvs|txt|last1=Atiyah|last2=Bott|last3=Garding|year1= 1970|year2=1973.

References

*Citation | last1=Atiyah | first1=Michael Francis | author1-link=Michael Atiyah | title=Séminaire Bourbaki, Vol. 10 | url= http://www.numdam.org/item?id=SB_1966-1968__10__87_0 | publisher=Société Mathématique de France | location=Paris | id=MathSciNet | id = 1610456 | year=1995 | chapter=Hyperbolic differential equations and algebraic geometry (after Petrowsky) | pages=87–99
*Citation | last1=Atiyah | first1=Michael Francis | author1-link=Michael Atiyah | last2=Bott | first2=Raoul | author2-link=Raoul Bott | last3=Garding | first3=L. | title=Lacunas for hyperbolic differential operators with constant coefficients. I | id=MathSciNet | id = 0470499 | year=1970 | journal=Acta Mathematica | issn=0001-5962 | volume=124 | pages=109–189|doi= 10.1007/BF02394570
*Citation | last1=Atiyah | first1=Michael Francis | author1-link=Michael Atiyah | last2=Bott | first2=Raoul | author2-link=Raoul Bott | last3=Garding | first3=L. | title=Lacunas for hyperbolic differential operators with constant coefficients. II | id=MathSciNet | id = 0470500 | year=1973 | journal=Acta Mathematica | issn=0001-5962 | volume=131 | pages=145–206|doi= 10.1007/BF02392039
*citation |last=Petrovsky|first=I. G. |title=On the diffusion of waves and the lacunas for hyperbolic equations|year=1945|journal=Mat. Sbornik|volume=17|pages=289–368


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