Brunn-Minkowski inequalities for variational functionals and related problems |
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Authors: | Andrea Colesanti |
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Institution: | Dipartimento di Matematicà “U. Dini”, Universita di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy |
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Abstract: | Recently, several inequalities of Brunn-Minkowski type have been proved for well-known functionals in the Calculus of Variations, e.g. the first eigenvalue of the Laplacian, the Newton capacity, the torsional rigidity and generalizations of these examples. In this paper, we add new contributions to this topic: in particular, we establish equality conditions in the case of the first eigenvalue of the Laplacian and of the torsional rigidity, and we prove a Brunn-Minkowski inequality for another class of variational functionals. Moreover, we describe the links between Brunn-Minkowski type inequalities and the resolution of Minkowski type problems. |
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Keywords: | 35J25 39B26 52A20 |
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