PageHeader : Funkcialaj Ekvacioj, 2 (1959), 27-70 Title : Principally Linear Partial Differential Title : Equations of Elliptic Type AuthorInfo : By Yoshikazu HIRASAWA AuthorInfo : (Kobe University) section : Introduction section : Chapter I. Preliminaries subsection : 1. Notations and preliminary remarks. subsection : 2. Generalizatioa of the operation of elliptic type3) subsection : 3. Summary about elementary solutions section : Chapter II. Theorems of comparison and conditions of uniqueness subsection : 4. Theorems of comparison. subsection : 5. Conditions of uniqueness section : Chapter III. Existence theorems, I subsection : 6. The equation $\mathfrak{L}(u)=f(x)$ . subsection : 7. Estimation of the derivatives $\partial_{x}u$ subsection : 8. The case where $f(x,u,p)$ is bounded. section : Chapter IV. Existence theorems, II subsection : 9. Introductive remarks. subsection : 10. Lemmas and a preliminary existence theorem. subsection : 11. Existence theorem for the general case. section : Chapter V. The maximal solution, the minimal solution, and Harnack's theorems subsection : 12. The maximal solution and the minimal solution. subsection : 13. Harnack's theorem. section : References section : Postskribo