The Curvature of a Set with Finite Area

Elisabetta Barozzi

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A comparison theorem for the Levi equation

Giovanna Citti (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove a strong comparison principle for the solution of the Levi equation $L (u) = \sum_{i = 1}^{n} ((1 + u_{t}^{2}) (u_{x_{i} x_{i}} + u_{y_{i} y_{i}}) + (u_{x_{i}}^{2} + u_{y_{i}}^{2}) u_{t t} + 2 (u_{y_{i}} - u_{x_{i}} u_{t}) u_{x_{i} t} - 2 (u_{x_{i}} + u_{y_{i}} u_{t}) u_{y_{i} t} + k (x, y, t) (1 + | D u |^{2})^{3 / 2} = 0$ , applying Bony Propagation Principle.