Geodesic
Weakly first-order interior estimates and Hessian equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 55-66

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The development of the modern theory of fully nonlinear second-order partial differential equations has amazingly enriched classic collection of ideas and methods. In this paper we construct the first-order interior a priori estimates of new type for solutions of Hessian equations and do it in order to present the most transparent version of Krylov's method and its tight connection with fully nonlinear equations. 
@article{ZNSL_2006_336_a3,
     author = {N. M. Ivochkina},
     title = {Weakly first-order interior estimates and {Hessian} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--66},
     publisher = {mathdoc},
     volume = {336},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a3/}
}
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N. M. Ivochkina. Weakly first-order interior estimates and Hessian equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Tome 336 (2006), pp. 55-66. http://geodesic.mathdoc.fr/item/ZNSL_2006_336_a3/