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Geometrical Aspects of Symmetrization

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Calculus of Variations and Nonlinear Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1927))

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Symmetrization is one of the most powerful mathematical tools with several applications both in Analysis and Geometry. Probably the most remarkable application of Steiner symmetrization of sets is the De Giorgi proof (see [14], [25]) of the isoperimetric property of the sphere, while the spherical symmetrization of functions has several applications to PDEs and Calculus of Variations and to integral inequalities of Poincaré and Sobolev type (see for instance [23], [24], [19], [20])

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II” Via Cintia, 80126, Napoli, Italy

    Nicola Fusco

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  1. Nicola Fusco
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Editors and Affiliations

  1. Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 8, 1015, Lausanne, Switzerland

    Bernard Dacorogna

  2. Dipartimento di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Paolo Marcellini

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Fusco, N. (2008). Geometrical Aspects of Symmetrization. In: Dacorogna, B., Marcellini, P. (eds) Calculus of Variations and Nonlinear Partial Differential Equations. Lecture Notes in Mathematics, vol 1927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75914-0_5

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