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Phragmén–Lindelöf type theorem for m-hessian equations

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We derive an interior estimate for the gradient of a solution u to the m-Hessian equation with a certain right-hand side. The estimate depends on the oscillation of u and properties of the right-hand side of the equation. The proof is based on a modification of some ideas of Trudinger (1997). As a consequence of the main result, a theorem of Fragmén–Lindelöf type is obtained for solutions to the m-Hessian equations in the entire space \( \mathbb{R}^n \). Bibliography: 4 titles.

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References

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Authors and Affiliations

  1. St. Petersburg State University of Architecture and Civil Engineering, 4, 2-nd Krasnoarmeiskaya Str., St. Petersburg, 190005, Russia

    N. V. Filimonenkova

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  1. N. V. Filimonenkova
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Correspondence to N. V. Filimonenkova.

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Translated from Problems in Mathematical Analysis 39 February, 2009, pp. 147–155.

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Filimonenkova, N.V. Phragmén–Lindelöf type theorem for m-hessian equations. J Math Sci 157, 948–957 (2009). https://doi.org/10.1007/s10958-009-9365-7

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  • DOI: https://doi.org/10.1007/s10958-009-9365-7

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