Explicit \(L^{\infty }\)-norm estimates via Morse index for the bi-harmonic and tri-harmonic semilinear problems



In this paper, we establish \(L^{\infty }\) and \(L^{p}\) estimates for solutions of some polyharmonic elliptic equations via the Morse index. As far as we know, it seems to be the first time that such explicit estimates are obtained for polyharmonic problems.

Mathematics Subject Classification

35J48 35J05 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ANLIG, UR13ES32University of Tunis El-ManarEl Manar IITunisia
  2. 2.Department of MathematicsNorthern Border UniversityArarSaudi Arabia
  3. 3.Institut de Mathématiques Appliquées et de l’InformatiqueUniversité de KairouanKairouanTunisia
  4. 4.IECL, UMR 7502Université de LorraineMetzFrance

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