A nonlinear bilaplacian equation with hinged boundary conditions and very weak solutions: analysis and numerical solution

  • Iñigo Arregui
  • Jesús Ildefonso Díaz
  • Carlos VázquezEmail author
Original Paper


We study linear and nonlinear bilaplacian problems with hinged boundary conditions and right hand side in \(L^{1}(\Omega :\delta )\), with \(\delta =\text{ dist }\,(x,\partial \Omega )\). More precisely, the existence and uniqueness of the very weak solution is obtained and some numerical techniques are proposed for its approximation.


Very weak solutions Distance to the boundary Nonlinear bilaplacian operator Hinged boundary conditions Numerical methods Finite elements 

Mathematics Subject Classification

35G50 35G60 74G25 74G15 


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Copyright information

© Springer-Verlag Italia 2013

Authors and Affiliations

  • Iñigo Arregui
    • 1
  • Jesús Ildefonso Díaz
    • 2
  • Carlos Vázquez
    • 1
    Email author
  1. 1.Department of Mathematics, Faculty of InformaticsUniversity of A Coruña CoruñaSpain
  2. 2.Department of Applied Mathematics, Instituto de Matemática InterdisciplinarComplutense University of Madrid MadridSpain

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