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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2002 | 78 | 3 | 277-289

## Laurent series expansion for solutions of hypoelliptic equations

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.

277-289

wydano
2002

### Twórcy

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