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Weak first-order interior estimates and Hessian equations

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Abstract

Development of the modern theory of fully nonlinear, second-order partial differential equations has amazingly enriched the classical collection of ideas and methods. In this paper, we construct first-order interior a priori estimates of new type for solutions of Hessian equations. These estmates are applied to present the most transparent version of Krylov’s method and its tight connection with fully nonlinear equations. Bibliography: 11 titles.

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Authors and Affiliations

  1. St.Petersburg State University of Architecture and Civil Engineering, Russia

    N. M. Ivochkina

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  1. N. M. Ivochkina
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 336, 2006, pp. 55–66.

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Ivochkina, N.M. Weak first-order interior estimates and Hessian equations. J Math Sci 143, 2875–2882 (2007). https://doi.org/10.1007/s10958-007-0173-7

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  • DOI: https://doi.org/10.1007/s10958-007-0173-7

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