Results 11 to 20 of about 200 (103)
On the continuity of the Continuous Steiner Symmetrization
, 2022 Starting from the Brock's construction of Continuous Steiner Symmetrization of sets, the problem of modifying continuously a given domain up to obtain a ball, preserving its measure and with decreasing first eigenvalue of the Laplace operator, is considered.
Buttazzo, Giuseppe
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An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2021 In this paper we consider the so-called procedure ofContinuous Steiner Symmetrization, introduced by Brock in [F. Brock,Math. Nachr.172(1995) 25–48 and F. Brock,Proc. Indian Acad. Sci.110(2000) 157–204]. It transforms every open set Ω ⊂⊂ ℝdinto the ball keeping the volume fixed and letting the first eigenvalue and the torsional rigidity respectively ...
Giuseppe Buttazzo, Aldo Pratelli
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Stability of the Steiner symmetrization of convex sets [PDF]
Journal of the European Mathematical Society, 2013 The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.
BARCHIESI, MARCO +2 more
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Steiner symmetric extremals in Pólya–Szegö-type inequalities
Advances in Mathematics, 2006 The aim of the present paper is to analyse the cases of equality in Steiner symmetrization inequalities for Dirichlet-type integrals. The results of the authors yield the Steiner symmetry of PS-extremals in the class of Sobolev, and more generally, BV functions, for a large class of functionals.
CIANCHI, ANDREA, N. FUSCO
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Poincaré inequalities and Steiner symmetrization
Illinois Journal of Mathematics, 1996 The domain \(\Omega\subset\mathbb{R}^n\) is said to be a \(p\)-Poincaré domain, \(1\leq pn-1\). The authors give also a more restricted class of Steiner symmetric domains for which the characterization remains valid for all \(p>1\).
Koskela, Pekka, Stanoyevitch, Alexander
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Steiner symmetrization using a finite set of directions
Advances in Applied Mathematics, 2012 Let $v_1, ..., v_m$ be a finite set of unit vectors in $\RR^n$. Suppose that an infinite sequence of Steiner symmetrizations are applied to a compact convex set $K$ in $\RR^n$, where each of the symmetrizations is taken with respect to a direction from among the $v_i$. Then the resulting sequence of Steiner symmetrals always converges, and the limiting
Klain, Daniel A., Daniel A. Klain
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On the continuity of the Continuous Steiner Symmetrization [PDF]
, 2023 Starting from the Brock's construction of Continuous Steiner Symmetrization of sets, the problem of modifying continuously a given domain up to obtain a ball, preserving its measure and with decreasing first eigenvalue of the Laplace operator, is considered.
Buttazzo
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The Non-Convergence of Steiner Symmetrizations
Wuhan University Journal of Natural Sciences, 2023 In this paper, we demonstrate the existence of iterated Steiner symmetrizations of [see formula in PDF] that does not converge, even if the sequence of directions is dense in the unit sphere.
Tian WANG, Youjiang LIN
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Steiner symmetrals and their distance from a ball [PDF]
Israel Journal of Mathematics, 2003 For \(\varepsilon> 0\), let \(N(n,\varepsilon)\) be the minimum number of successive Steiner symmetrizations sufficient to transform any convex body in \(\mathbb{R}^n\), with volume equal to the volume of the unit ball \(B^n\), into a convex body whose Hausdorff distance from \(B^n\) is at most \(\varepsilon\).
BIANCHI, GABRIELE, GRONCHI, PAOLO
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