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Neumann Problems and Steiner Symmetrization

Communications in Partial Differential Equations, 2005
ABSTRACT In the present paper we prove some comparison results via Steiner symmetrization for solutions to the Neumann problem where T > 0, Ω is a smooth connected open bounded subset of ℝ n , the coefficients a ij (x, y) and the datum f are smooth functions such that a ij (x, y)ξ i ξ j  ≥ |ξ|2, for any (x, y) ∈ G, for any ξ ∈ ℝ n and ∈ t G f dx dy = 0.
Vincenzo Ferone
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Steiner Symmetrization is Continuous in W 1, p

Geometric and Functional Analysis, 1997
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Almut Burchard
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Elliptic equations and Steiner symmetrization

Communications on Pure and Applied Mathematics, 1996
Let \(G\) be an open bounded subset of \(\mathbb{R}^N\) and \(u\) a function defined on \(\overline G\). Then the function \(u^*(s)= \sup\{t\geq 0: \mu(t)> s\}\), where \(\mu\) is the distribution function of \(u\), is known as the decreasing rearrangement of \(u\).
Jesus Ildefonso Diaz
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On the topology of the Steiner symmetrization mapping

Journal of Mathematical Sciences, 1996
We prove that the Steiner symmetrization mapping on the hyperspace of convex bodies in ℝ2 is soft and homeomorphic to a fibration in the bundle of Q-manifolds over any compact subset in the hyperspace of symmetric nonpolyhedral subsets.
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Weighted Dirichlet-type inequalities for Steiner symmetrization

Calculus of Variations and Partial Differential Equations, 1999
The following type of inequality is proved: \[ \int_{\mathbb{R}^{N}}F(x,u^{\ast },|\nabla u^{\ast }|) dx\leq \int_{\mathbb{R}^{N}}F(x,u,|\nabla u|) dx, \tag{1} \] where \(u\in W_{+}^{1,p}(\mathbb{R}^{N})\), \(1\leq p1\) and especially for \(F(x,u,z)=|z|^{p}\). See for related results: \textit{A. Alvino, P.-L. Lions} and \textit{G. Trombetti} [Nonlinear
F Brock
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Steiner Symmetrization

2019
Albert Baernstein
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Steiner Symmetrization

1999
Harold R Parks
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STEINER SYMMETRIZATION AND THE CONFORMAL MODULI OF PARALLELOGRAMS

1998
Edgar Reich
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Continuous Steiner‐Symmetrization

Mathematische Nachrichten, 1995
Summary: For nonnegative \(L\)-measurable functions \(u:\mathbb{R}^n\to\mathbb{R}\) a continuous homotopy \(u^t\), \(0\leq t\leq+\infty\), is constructed, connecting \(u\) with its Steiner-symmetrization \(u^*\). It is shown that a number of familiar relations between \(u\) and \(u^*\) including some integral inequalities are also valid for \(u\) and \(
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Smoothness of the Steiner symmetrization

Proceedings of the American Mathematical Society, 2017
In the \(n\)-dimensional Euclidean space \(\mathbb{R}^n\), let \(K\) be a compact convex subset, and let \(K_1\) be the Steiner symmetral of \(K\) with respect to the hyperplane \(e_1^{\perp}\), orthogonal to a unit vector \(e_1\in\mathbb{R}^n\). Namely, \(K_1\) is obtained by translating all the chords of \(K\) in direction \(e_1\), so that their ...
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