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. 
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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/

[1] N. V. Krylov, “Unconditional solvability of the Bellman equations with constant coefficients in convex domains”, Math. USSR-Sb., 63:2 (1989), 289–303 | DOI | MR | Zbl

[2] N. V. Krylov, “Weak interior second order derivative estimates for degenerate for nonlinear elliptic equations”, Diff. Int. Eqns., 7 (1994), 133–156 | MR | Zbl

[3] N. V. Krylov, Lectures on fully nonlinear second order elliptic equations, Rudolph–Lipschitz–Vorlesung, No 29, Vorlesungsreihe, Rheinische Friedrich–Wilhelms–Universitat, Bonn, 1994

[4] N. M. Ivochkina, N. Trudinger, X.-J. Wand, “The Dirichlet problem for degenerate Hessian equations”, Comm. Part. Diff. Eqns., 29 (2004), 219–235 | DOI | MR | Zbl

[5] L. Caffarelli, L. Nirenberg, J. Spruck, “Dirichlet problem for nonlinear second order elliptic equations III: Functions of the eigenvalues of the Hessian”, Acta Math., 155 (1985), 261–301 | DOI | MR | Zbl

[6] N. S. Trudinger, “On the Dirichlet problem for Hessian equations”, Acta Math., 175 (1995), 151–164 | DOI | MR | Zbl

[7] Math. USSR Sb., 50 (1985), 259–268 | DOI | MR | Zbl

[8] L. Garding, “An inequality for hyperbolic polynomials”, J. Math. Mech., 8 (1959), 957–965 | MR | Zbl

[9] M. G. Crandall, “Semidifferential quadratic forms and fully nonlinear elliptic equations of second order”, Ann. Inst. H. Poincare Anal. Non Lineaire, 6 (1989), 419–435 | MR | Zbl

[10] J. Math. Sci., 101 (2000), 3503–3511 | DOI | MR | Zbl

[11] St. Petersburg Math. J., 4 (1993), 1169–1189 | MR | Zbl