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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Fully nonlinear, uniformly elliptic equations under natural structure conditions

Author: Neil S. Trudinger
Journal: Trans. Amer. Math. Soc. 278 (1983), 751-769
MSC: Primary 35J60; Secondary 49C20
MathSciNet review: 701522
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Abstract: We derive first and second derivative estimates for classical solutions of fully nonlinear, uniformly elliptic equations which are subject to natural structure conditions analogous to those proposed and treated by Ladyzhenskaya and Ural'tseva for quasilinear equations. As an application we extend recent work of Evans and Lions on the Bellman equation for families of linear operators to families of quasilinear operators.

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