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2 results

  • On second derivative estimates for equations of Monge-Ampère type

  • Neil S. Trudinger, John I.E. Urbas
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 30 / Issue 3 / December 1984
    Published online by Cambridge University Press:
    17 April 2009, pp. 321-334
    Print publication:
    December 1984
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  • We derive interior second derivative estimates for solutions of equations of Monge-Ampère type which extend those of Pogorelov for the case of affine boundary values. A key ingredient in our method is the existence of a strong solution of the homogeneous Monge-Ampère equation.

  • The Dirichlet problem for the equation of prescribed Gauss curvature

  • Neil S. Trudinger, John I.E. Urbas
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 28 / Issue 2 / October 1983
    Published online by Cambridge University Press:
    17 April 2009, pp. 217-231
    Print publication:
    October 1983
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  • We treat necessary and sufficient conditions for the classical solvability of the Dirichlet problem for the equation of prescribed Gauss curvature in uniformly convex domains in Euclidean n space. Our methods simultaneously embrace more general equations of Monge-Ampère type and we establish conditions which ensure that solutions have globally bounded second derivatives.