Symmetrization and Applications

By S. Kesavan. 2006

230 citations recorded by the source corpus.

Subfields: Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/e7f01e46b7c8a9b15869a3f9fedf8cf72e1efcd0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Physical and Theoretical Chemistry

Citations in the corpus

New approach to the affine P\'olya-Szeg\"o principle and the stability version of the affine Sobolev inequality (2015, background): “They are affine analogues of the classical Pólya-Szegö principle [55] which plays a fundamental role in the solution of several variational problems from different areas such as isoperimetric inequalities, sharp forms of Sobolev inequalities and sharp a priori estimates of solutions to second-order ”
On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique (2014, background): “The reader is referred to [16], Chapter 2 or [17], Chapters 1 and 2, for more details on the Schwarz symmetrization and the Pólya–Szegő principle.”
An asymmetric affine Pólya–Szegö principle (2012, background): “, [3,8,20,25,26,42,58,67,71]), and the references therein).”
Wulff shape characterizations in overdetermined anisotropic elliptic problems (2017, background): “Symmetry results for problems involving (Euclidean) capacity go back to Pólya and Szegö and subsequents authors (see for instance [51, 43, 40, 31, 58, 59] and references therein).”
An Isoperimetric Inequality for Fundamental Tones of Free Plates (2010, background): “, we gather some calculus facts used in prior chapters. Brief history of isoperimetric problems Isoperimetric problems for eigenvalues of the Laplacian have fascinated researchers for quite some time [3, 5, 10, 17, 20, 22, 54]. In 1877, Lord Rayleigh [43] conjectured an isoperimetric inequality for ”
Sharp singular Adams inequalities in high order Sobolev spaces (2011, result): “Now, we state the following known result from [12, 25]: Lemma 2.”
Eigenvalues of poly-harmonic operators on variable domains (2012, methodology): “We refer to Bucur and Buttazzo [4], Daners [10], Hale [13], Henry [15], Henrot [14], Kesavan [18] for updated information on this topic.”
Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions (2014, unknown): “t, that is Ω∗ = B R(0),where |Ω| = πR2.If u ∈ W1,2 0 (Ω),then u∗ ∈ W1,2 0,radց(BR(0)) will denote the Schwarz symmetrization of u.For basic propertis of the Schwarz symmetrization we refer to Kesavan [7], Chapters 1 and 2, which we will use throughout. In particular we will use frequently and withou”
Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves (2008, unknown): “[15]).”