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Semilinear subelliptic problems without compactness on Lie groups

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

An abstract version of concentration compactness on Hilbert spaces applies to to actions of non-compact Lie groups. Using the concentration compactness argument we prove existence of solutions for semilinear problems involving sub-Laplacians on the whole Lie group and on their cer-tain non-compact subsets, including minimizers for Sobolev inequalities. The result is stated for any real connected finite-dimensional Lie group.

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Authors and Affiliations

  1. Ceremath, University of Toulouse I, Toulouse Cedex4, France

    I. Schindler

  2. UMR MIP CNRS 5640, Université Paul Sabatier, Toulouse Cedex4, France

    I. Schindler

  3. Uppsala University, Uppsala, Sweden

    K. Tintarev

Authors
  1. I. Schindler
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  2. K. Tintarev
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Correspondence to I. Schindler.

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Schindler, I., Tintarev, K. Semilinear subelliptic problems without compactness on Lie groups. Nonlinear differ. equ. appl. 11, 299–309 (2004). https://doi.org/10.1007/s00030-004-1059-0

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  • DOI: https://doi.org/10.1007/s00030-004-1059-0

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