The Dirichlet Problem for Nonuniformly Elliptic Equations

  title={The Dirichlet Problem for Nonuniformly Elliptic Equations},
  author={Neil S. Trudinger},
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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