Advances in Differential Equations

Strong solutions for the Levi curvature equation

G. Citti and A. Montanari

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We consider the prescribed Levi curvature equation, a second order quasilinear equation whose associated operator can be represented as a sum of squares of nonlinear vector fields. For this equation we introduce a notion of derivatives modeled on the geometry of the associated operator and prove an a priori $L^2$ estimate for these second order intrinsic derivatives of a viscosity solution. We then show that viscosity solutions are strong solutions in a natural sense and satisfy the equation almost everywhere.

Article information

Adv. Differential Equations, Volume 5, Number 1-3 (2000), 323-342.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 32F99: None of the above, but in this section 35J70: Degenerate elliptic equations


Citti, G.; Montanari, A. Strong solutions for the Levi curvature equation. Adv. Differential Equations 5 (2000), no. 1-3, 323--342.

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