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. { Certain fundamental solutions E a of the partial dierential operators@31 + @32 + @33 + 3a@ 1 @ 2 @ 3 ; a 2 R n f1g; are represented by elliptic integrals of the rstkind. These operators are (apart from a linear change of variables) the most generalhomogeneous operators of real principal type in three variables and irreducible of degreethree. The fundamental solutions E a show interesting non-convex lacunas, and theirremaining level sets are algebraic surfaces of degree 6,...

Fundamental solutions of real homogeneous cubic operators of principal type in three dimensions