On the hypoellipticity of differential forms with isolated singularities

摘要

Hypoellipticity for a class of germs of □-valued, real-analytic 1-forms with an isolated singularity is studied. The main result states that in dimension ≥3 such forms are real-analytic hypoelliptic over L ~p functions, but are not real-analytic hypoelliptic in dimension 2. The case of C ~∞-hypoellipticity for a class of rotation invariant forms in □~2 is also considered.