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On Caffarelli–Kohn–Nirenberg-type Inequalities for the Weighted Biharmonic Operator in Cones

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Abstract

We investigate Caffarelli–Kohn–Nirenberg-type inequalities for the weighted biharmonic operator in cones, both under Navier and Dirichlet boundary conditions. Moreover, we study existence and qualitative properties of extremal functions. In particular, we show that in some cases extremal functions do change sign; when the domain is the whole space, we prove some breaking symmetry phenomena.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, via Carlo Alberto, 10, 10123, Torino, Italy

    Paolo Caldiroli

  2. Dipartimento di Matematica ed Informatica, Università di Udine, via delle Scienze, 206, 33100, Udine, Italy

    Roberta Musina

Authors
  1. Paolo Caldiroli
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  2. Roberta Musina
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Correspondence to Paolo Caldiroli.

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Caldiroli, P., Musina, R. On Caffarelli–Kohn–Nirenberg-type Inequalities for the Weighted Biharmonic Operator in Cones. Milan J. Math. 79, 657–687 (2011). https://doi.org/10.1007/s00032-011-0167-2

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  • DOI: https://doi.org/10.1007/s00032-011-0167-2

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