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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On the general notion of fully nonlinear second-order elliptic equations


Author: N. V. Krylov
Journal: Trans. Amer. Math. Soc. 347 (1995), 857-895
MSC: Primary 35J60; Secondary 35J65
MathSciNet review: 1284912
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Abstract: The general notion of fully nonlinear second-order elliptic equation is given. Its relation to so-called Bellman equations is investigated. A general existence theorem for the equations like $ {P_m}({u_{{x^i}{x^j}}}) = \sum\nolimits_{k = 0}^{m - 1} {{c_k}(x){P_k}({u_{{x^i}{x^j}}})} $ is obtained as an example of an application of the general notion of fully nonlinear elliptic equations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1284912-8
PII: S 0002-9947(1995)1284912-8
Article copyright: © Copyright 1995 American Mathematical Society