Journal d’Analyse Mathématique

, Volume 84, Issue 1, pp 1–49 | Cite as

Nonexistence results and estimates for some nonlinear elliptic problems

  • Marie-Francoise Bidaut-Véron
  • Stanislav Pohozaev


Here we study the local or global behaviour of the solutions of elliptic inequalities involving quasilinear operators of the type\(L_{\mathcal{A}^u } = - div\left[ {\mathcal{A}\left( {x,u,\nabla u} \right)} \right] \geqslant \left| x \right|^\sigma u^Q \) or\(\begin{gathered} L_{\mathcal{A}^u } = - div\left[ {\mathcal{A}\left( {x,u,\nabla u} \right)} \right] \geqslant \left| x \right|^\sigma u^S v^R \hfill \\ L_{\mathcal{B}^u } = - div\left[ {\mathcal{B}\left( {x,u,\nabla u} \right)} \right] \geqslant \left| x \right|^b u^Q u^T \hfill \\ \end{gathered} \). We give integral estimates and nonexistence results. They depend on properties of the supersolutions of the equationsL A u=0,L B v=0, which suppose weak coercivity conditions. Under stronger conditions, we give pointwise estimates in case of equalities, using Harnack properties.


Harnack Inequality Nonnegative Solution Radial Solution Integral Estimate Strong Maximum Principle 
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Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  • Marie-Francoise Bidaut-Véron
    • 1
  • Stanislav Pohozaev
    • 2
  1. 1.CNRS UPRES-A 6083 Faculté des SciencesLaboratoire de Mathématiques et Physique ThéoriqueToursFrance
  2. 2.Steklov Mathematical InstituteMoscowRussia

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