## The Dirichlet problem for nonlinear second order elliptic equations , III : Functions of the eigenvalues of the Hessian

- Luis Caffarelli, L. NIRENBERG, J. SPRUCK
- 2006

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@inproceedings{Trudinger2007TheDP, title={The Dirichlet Problem for Nonuniformly Elliptic Equations}, author={Neil S. Trudinger}, year={2007} }

- Published 2007

and repeated indices indicate summation from 1 to n. The functions a'(x, u, p), a(x, u, p) are defined in QX£ n + 1 . If furthermore for any ikf>0, the ratio of the maximum to minimum eigenvalues of [a(Xy u, p)] is bounded in ÛX( — M, M)XE, Qu is called uniformly elliptic. A solution of the Dirichlet problem Qu = Q, u—<f)(x) on <50 is a C(n)P\C(O) function u(x) satisfying Qu = 0 in £2 and agreeing with <f>(x) on 30. When Qu is elliptic, but not necessarily uniformly elliptic, it is referred to… CONTINUE READING

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