Abstract

This paper is concerned with the solvability of a class of nonlinear variational inequalities involving pointwise unilateral constraints on the laplacian. We describe the set of the pairs (ψ,h) of the right hand sides h and the obstacles ψ for which the problem has solutions and study the structure of the set of solutions. The existence and multiplicity results we obtain point out that the presence of the obstacle gives rise to some phenomena which are typical of the semilinear elliptic equations with "jumping" nonlinearities.

Author information

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Riccardo Molle

Dip. di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

Donato Passaseo

Dip. di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

Keywords

  • Variational problems
  • topological methods
  • pointwise constraints on the laplacian
  • nonsmooth analysis
  • subgradients

Mathematics Subject Classification

35J20; 35R45, 45J10

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Suggested citation

R. Molle, D. Passaseo. “Variational Problems with Pointwise Constraints on the Derivatives.” Journal of Convex Analysis 6 (1999), No. 2, 215–233. https://doi.org/10.68381/jca06014

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Published by Heldermann Verlag, 1999. Rights now held by Banach Press LLC.