Nonlinear flows and optimality for functional inequalities : an extended abstract
Esteban, Maria J. (2017), Nonlinear flows and optimality for functional inequalities : an extended abstract, in Pammy Manchanda, René Lozi, Abul Hasan Siddiqi, Industrial Mathematics and Complex Systems, Springer : Berlin Heidelberg, p. 21-26. 10.1007/978-981-10-3758-0
Book titleIndustrial Mathematics and Complex Systems
Book authorPammy Manchanda, René Lozi, Abul Hasan Siddiqi
Series titleIndustrial and Applied Mathematics
Number of pages357
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Author(s)Esteban, Maria J.
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)The talk given on the occasion of the ISIAM 2016 conference was mainly about rigidity results for nonnegative solutions of semilinear elliptic equation on infinite cylinder-like domains or in the Euclidean espace and as a consequence, about optimal symmetry properties for the optimizers of the Caffarelli–Kohn–Nirenberg inequalities. This text contains the main results presented in that conference. All the results will be stated in the simple case of spherical cylinders, but similar, even if less precise, results can also be stated and proved for general cylinders generated by any compact smooth Riemannian manifold without a boundary. Other consequences from the results below are optimal estimates for the principal eigenvalue of Schrödinger operators on infinite cylinders. The text below is an extended abstract of that talk.
Subjects / KeywordsCaffarelli–Kohn–Nirenberg inequalities; Symmetry; Symmetry breaking; Optimal constants; Rigidity results; Fast diffusion equation; Carré du champ; Bifurcation; Instability; Emden–Fowler transformation; Cylinders; Noncompact manifolds; Laplace–Beltrami operator; Spectral estimates; Keller–Lieb–Thirring estimate; Hardy inequality
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