Abstract
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.
Citation
G. Citti. A. Montanari. "Strong solutions for the Levi curvature equation." Adv. Differential Equations 5 (1-3) 323 - 342, 2000. https://doi.org/10.57262/ade/1356651387
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