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Sulla integrazione della equazione di Hamilton-Jacobi per separazione di variabili. (Italian) JFM 35.0362.02
Die Abhandlung knüpft an die gleichlautende Habilitationsschrift von Stäckel an (F. d. M. 23, 402, 1891, JFM 23.0402.02); es wird in einfacher Weise gezeigt, daß die Hamilton-Jacobische Differentialgleichung \[ H(p_1,\dots,p_n,\, x_1,\dots,x_n) = h \] durch Separation der Variabeln dann und nur dann lösbar ist, wenn die charakteristischen \(H\) den \(\frac12n(n - 1)\) Gleichungen vom zweiten Grade \[ \begin{split} \frac{\partial H}{\partial p_i} \frac{\partial H}{\partial p_j} \frac{\partial^2H}{\partial x_i\partial x_j} - \frac{\partial H}{\partial p_i} \frac{\partial H}{\partial x_j} \frac{\partial^2H}{\partial x_i\partial p_j} - \frac{\partial H}{\partial x_i} \frac{\partial H}{\partial p_j} \frac{\partial^2H}{\partial p_i\partial x_j}\\ + \frac{\partial H}{\partial x_i}\cdot \frac{\partial H}{\partial x_j} \frac{\partial^2H}{\partial p_i\partial p_j} = 0\quad (i\gtrless j)\end{split} \] genügen. Verschiedene Folgerungen allgemeiner Art ergeben sich dann noch aus diesen Bedingungen.

Subjects:
Sechster Abschnitt. Differential- und Integralrechnung. Kapitel 6. Partielle Differentialgleichungen.
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References:
[1] Habilitationsschrift, Halle 1891; od anche Mathem. Annalen, Bd. XLII, S. 546-549.
[2] Atti della R. Accademia di Torino, Vol. XVI, 1881.
[3] Mathem. Annalen, Bd. XXXV.
[4] Habilitationsschrift, S. 8; Math. Annalen, Bd. XLII, S. 548.
[5] ?Lezioni sulla teoria delle superficie?, Padova 1898, presso Drucker; Cap. V.
[6] Math. Ann., Bd. XXXV, S. 94.
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