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Steiner symmetrization and the eigenvalues of the Laplace operator on polygons
, 2021 The topic that I chose to explore for this thesis is a study of the eigenvalues of the Dirichlet Laplacian on a two dimensional domain and the properties that arise as a direct consequence to them. The eigenvalues of a given domain pro- duce so many surprising insights that simply the study of a triangular domain has many directions in which one could ...
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Steiner symmetrization and applications
, 2005 Proceedings of "The Renato Caccioppoli Centenary Conference", Napoli ...
FERONE, VINCENZO
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STEINER SYMMETRIZATION AND THE CONFORMAL MODULI OF PARALLELOGRAMS
1998Edgar Reich
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On iterations of Steiner symmetrizations
Annali di Matematica Pura ed Applicata (1923 -), 2015Let \(N\) be a positive integer and let \(u \in \mathbb{S}^{N-1} := \{ x \in \mathbb{R}^N : \| x \| = 1 \}\) denote the unit sphere. The \textit{Steiner symmetrization} in the direction \(u\) is a mapping \(S_u\) of measurable subsets of \(\mathbb{R}^N\) to measurable subsets of \(\mathbb{R}^N\), acting as follows.
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Symmetric abelian group-invariant Steiner quadruple systems
Journal of Combinatorial Theory, Series A, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lijun Ji, Xiao-Nan Lu
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Partial Steiner symmetrization and some conduction problems
Journal of Mathematical Analysis and Applications, 1967 A Mcnabb
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Quantitative Steiner/Schwarz-type symmetrizations
Geometriae Dedicata, 1996Considering higher dimensional symmetrizations the author shows that very few of them suffice to bring a symmetric convex body close to a Euclidean ball. Further, the author proves that very few Schwarz symmetrizations suffice to bring a body to a distance at most \(1 + \varepsilon\) for every given \(\varepsilon\).
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Stability for the Dirichlet Problem under Continuous Steiner Symmetrization
Potential Analysis, 2000The authors present a nice construction that deforms an arbitrary open set into a ball. During the transformation the measure of the set stays invariant, the first Dirichlet-Laplace eigenvalue keeps decreasing, and the \(k\)-th eigenvalue is continuous from the left.
Bucur, Dorin, Henrot, Antoine
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Random Steiner symmetrizations of sets and functions
Calculus of Variations and Partial Differential Equations, 2012Let \(\mathcal{L}^N\) be the \(N\)-dimensional Lebesgue measure and \(\mathcal{M}\) be the family of all measurable sets of the \(N\)-dimensional Euclidean space \({\mathbb R}^N\) having finite measure. Denote by \(B(x, \rho)\) the closed ball centered at \(x\) having radius \(\rho\). The unit sphere of \({\mathbb R}^N\), that is the set of all vectors
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