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Symmetrization with respect to the anisotropic perimeter and applications

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Abstract

In this paper we introduce a new type of symmetrization, which preserves the anisotropic perimeter of the level sets of a suitable concave smooth function, in order to prove sharp comparison results for solutions of a class of homogeneous Dirichlet fully nonlinear elliptic problems of second order and for suitable anisotropic Hessian integrals.

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Acknowledgments

This work has been partially supported by the FIRB 2013 project “Geometrical and qualitative aspects of PDE’s” and by GNAMPA of INDAM.

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  1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Complesso di Monte Sant’Angelo, Università degli studi di Napoli Federico II, Via Cintia, 80126, Naples, Italy

    Francesco Della Pietra & Nunzia Gavitone

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  1. Francesco Della Pietra
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  2. Nunzia Gavitone
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Correspondence to Francesco Della Pietra.

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Della Pietra, F., Gavitone, N. Symmetrization with respect to the anisotropic perimeter and applications. Math. Ann. 363, 953–971 (2015). https://doi.org/10.1007/s00208-015-1191-2

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  • DOI: https://doi.org/10.1007/s00208-015-1191-2

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