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Asymptotic behavior and uniqueness of blow-up solutions of quasilinear elliptic equations

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Abstract

In this paper, we study the asymptotic behavior of solutions of the problem Δ p u = f (u) in Ω, u = ∞ on ∂Ω, under general conditions on the function f, where Ω p is the p-Laplace operator. We show that the technique used by the author for the special case p = 2 works in this more general setting, and that the behavior described by various authors for the case p = 2 is easily derived from this technique for the general case.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, Iowa, 50011, USA

    Gary M. Lieberman

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  1. Gary M. Lieberman
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Additional information

This paper was written at the Centre for Mathematics and its Applications, at the Australian National University while the author was on a Faculty Professional Development Assignment.

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Lieberman, G.M. Asymptotic behavior and uniqueness of blow-up solutions of quasilinear elliptic equations. JAMA 115, 213–249 (2011). https://doi.org/10.1007/s11854-011-0028-5

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  • DOI: https://doi.org/10.1007/s11854-011-0028-5

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