Laurent series expansion for solutions of hypoelliptic equations

• Autorzy: M. Langenbruch
• Języki publikacji: EN

Abstrakty

EN

We prove that any zero solution of a hypoelliptic partial differential operator can be expanded in a generalized Laurent series near a point singularity if and only if the operator is semielliptic. Moreover, the coefficients may be calculated by means of a Cauchy integral type formula. In particular, we obtain explicit expansions for the solutions of the heat equation near a point singularity. To prove the necessity of semiellipticity, we additionally assume that the index of hypoellipticity with respect to some variable is 1.

Kategorie tematyczne

• 35E20: General theory
• 35H10: Hypoelliptic equations
• 35C10: Series solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 78
• Numer: 3
• Strony: 277-289

Daty

wydano

2002

Twórcy

autor

M. Langenbruch

• Department of Mathematics, University of Oldenburg, D-26111 Oldenburg, Germany

Identyfikatory

DOI

10.4064/ap78-3-6