Displaying similar documents to “Regularity of potentials and removability of singularities of solutions of partial differential equations”

Laurent series expansion for solutions of hypoelliptic equations

M. Langenbruch (2002)

Annales Polonici Mathematici

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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...