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An improved Hardy-Sobolev inequality in W1,p and its application to Schrödinger operators

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

In this paper we prove new Hardy-like inequalities with optimal potential singularities for functions in W1,p(Ω), where Ω is either bounded or the whole space \(\mathbb{R}^n \) and also some extensions to arbitrary Riemannian manifolds. We also study the spectrum of perturbed Schrödinger operators for perturbations which are just below the optimality threshold for the corresponding Hardy inequality.

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Authors and Affiliations

  1. TIFR Centre, IISc Campus, P.B. Box 1234, Bangalore, 560 012, India

      Adimurthi

  2. CEREMADE, Université Paris IX-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Maria J. Esteban

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  1.   Adimurthi
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  2. Maria J. Esteban
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Correspondence to   Adimurthi.

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Adimurthi,  ., Esteban, M.J. An improved Hardy-Sobolev inequality in W1,p and its application to Schrödinger operators. Nonlinear differ. equ. appl. 12, 243–263 (2005). https://doi.org/10.1007/s00030-005-0009-4

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  • DOI: https://doi.org/10.1007/s00030-005-0009-4

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