Laurent series expansion for solutions of hypoelliptic equations

M. Langenbruch. "Laurent series expansion for solutions of hypoelliptic equations." Annales Polonici Mathematici 78.3 (2002): 277-289. <http://eudml.org/doc/280792>.

@article{M2002,
abstract = {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.},
author = {M. Langenbruch},
journal = {Annales Polonici Mathematici},
keywords = {isolated singularities; semielliptic operators; heat equation},
language = {eng},
number = {3},
pages = {277-289},
title = {Laurent series expansion for solutions of hypoelliptic equations},
url = {http://eudml.org/doc/280792},
volume = {78},
year = {2002},
}

TY - JOUR
AU - M. Langenbruch
TI - Laurent series expansion for solutions of hypoelliptic equations
JO - Annales Polonici Mathematici
PY - 2002
VL - 78
IS - 3
SP - 277
EP - 289
AB - 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.
LA - eng
KW - isolated singularities; semielliptic operators; heat equation
UR - http://eudml.org/doc/280792
ER -