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On nonlinear eigenvalue problems which extend into free boundaries problems

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Bifurcation and Nonlinear Eigenvalue Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 782))

Abstract

We consider a class of nonlinear elliptic eigenvalue problems, in an arbitrary bounded regular domain in ℝn, with multiple bending points (infinite in some cases). We associate with them a family of perturbed problems; the study of the corresponding singular perturbation enables us to extend the limiting elliptic problem into a free boundary problem. The latter also admits an infinite number of free boundary solutions in some cases of hyperspherical geometries.

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C. Bardos J. M. Lasry M. Schatzman

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© 1980 Springer-Verlag

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Brauner, C.M., Nicolaenko, B. (1980). On nonlinear eigenvalue problems which extend into free boundaries problems. In: Bardos, C., Lasry, J.M., Schatzman, M. (eds) Bifurcation and Nonlinear Eigenvalue Problems. Lecture Notes in Mathematics, vol 782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090428

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  • DOI: https://doi.org/10.1007/BFb0090428

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  • Print ISBN: 978-3-540-09758-7

  • Online ISBN: 978-3-540-38637-7

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