The Dirichlet Problem For The Prescribed Curvature Quotient Equations With General Boundary Values

Mathematics Research Report MRR95-087

The Dirichlet Problem For The Prescribed Curvature Quotient Equations With General Boundary Values

Nina M. Ivochkina, Mi Lin and Neil S. Trudinger

Abstract: We prove the classical solvability of the Dirichlet problem of prescribed curvature equations, for curvatures given by quotients of elementary symmetric functions of principal curvatures and general boundary values. Our results extend the case of constant boundary values due to Lin and Trudinger as well as earlier research of Ivochkina on the higher order mean curvature equations.

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