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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Poutala, Arto Tarhasaari, Timo and Kettunen, Lauri 2016. Geometric solution strategy of Laplace problems with free boundary. International Journal for Numerical Methods in Engineering, Vol. 105, Issue. 10, p. 723.

    Padial, J.F. 2007. On some nonlinear elliptic problems with an unknown measure data. PAMM, Vol. 7, Issue. 1, p. 2040037.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 137, Issue 5
  • October 2007, pp. 895-911

On some Bernoulli free boundary type problems for general elliptic operators

  • J. I. Díaz (a1), J. F. Padial (a2) and J. M. Rakotoson (a3)
  • DOI:
  • Published online: 01 September 2007

We consider some Bernoulli free boundary type problems for a general class of quasilinear elliptic (pseudomonotone) operators involving measures depending on unknown solutions. We treat those problems by applying the Ambrosetti–Rabinowitz minimax theorem to a sequence of approximate nonsingular problems and passing to the limit by some a priori estimates. We show, by means of some capacity results, that sometimes the measures are regular. Finally, we give some qualitative properties of the solutions and, for a special case, we construct a continuum of solutions.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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