Advances in Differential Equations

Nonlinear oblique boundary value problems for two-dimensional curvature equations

John Urbas

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We prove the existence of smooth solutions of two-dimensional nonuniformly elliptic curvature equations subject to a nonlinear oblique boundary condition. These are equations whose principal part is given by a suitable symmetric function of the principal curvatures of the graph of the solution $u$. The types of boundary conditions we are able to treat are the same as those we considered in earlier work on Hessian equations.

Article information

Adv. Differential Equations, Volume 1, Number 3 (1996), 301-336.

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]


Urbas, John. Nonlinear oblique boundary value problems for two-dimensional curvature equations. Adv. Differential Equations 1 (1996), no. 3, 301--336.

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