ON THE SOLUBILITY OF DIFFERENTIAL EQUATIONS WITH SIMPLE CHARACTERISTICS
Yu. V. Egorov · Russian Mathematical Surveys · 1971
A survey is given of papers devoted to the problem of the existence of solutions to linear differential and pseudo-differential equations of principal type. The main results in this field are due to Lewy, Hormander, Nirenberg, Treves and the author. We also give a new theorem of maximal generality on local solubility of equations of principal type. By way of illustration to the exposition we mention as examples: the Lewy operator; the operator arising from the solution of the problem with directional derivatives for elliptic second order equations; non-singular operators.