caa a22 4500 445843748 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00526-011-0394-y doi (NATIONALLICENCE)springer-10.1007/s00526-011-0394-y Radial symmetry and symmetry breaking for some interpolation inequalities [Elektronische Daten] [Jean Dolbeault, Maria Esteban, Gabriella Tarantello, Achilles Tertikas] We analyze the radial symmetry of extremals for a class of interpolation inequalities known as Caffarelli-Kohn-Nirenberg inequalities, and for a class of weighted logarithmic Hardy inequalities which appear as limiting cases of the first ones. In both classes we show that there exists a continuous surface that splits the set of admissible parameters into a region where extremals are symmetric and a region where symmetry breaking occurs. In previous results, the symmetry breaking region was identified by showing the linear instability of the radial extremals. Here we prove that symmetry can be broken even within the set of parameters where radial extremals correspond to local minima for the variational problem associated with the inequality. For interpolation inequalities, such a symmetry breaking phenomenon is entirely new. Springer-Verlag, 2011 Dolbeault Jean Ceremade, Univ. Paris-Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cédex 16, France aut Esteban Maria Ceremade, Univ. Paris-Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cédex 16, France aut Tarantello Gabriella Dipartimento di Matematica, Univ. di Roma "Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy aut Tertikas Achilles Department of Mathematics, University of Crete, Knossos Avenue, 714 09, Heraklion, Crete, Greece aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 461-485 0944-2669 42:3-4<461 2011 42 526 https://doi.org/10.1007/s00526-011-0394-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-011-0394-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dolbeault Jean Ceremade, Univ. Paris-Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cédex 16, France aut NATIONALLICENCE 700 1- Esteban Maria Ceremade, Univ. Paris-Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cédex 16, France aut NATIONALLICENCE 700 1- Tarantello Gabriella Dipartimento di Matematica, Univ. di Roma "Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Tertikas Achilles Department of Mathematics, University of Crete, Knossos Avenue, 714 09, Heraklion, Crete, Greece aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 461-485 0944-2669 42:3-4<461 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer