Open Access

Second-order estimates for boundary blowup solutions of special elliptic equations

Boundary Value Problems20062006:45859

DOI: 10.1155/BVP/2006/45859

Received: 20 October 2005

Accepted: 7 November 2005

Published: 2 March 2006

Abstract

We find a second-order approximation of the boundary blowup solution of the equation , with , in a bounded smooth domain . Furthermore, we consider the equation . In both cases, we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary .

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Authors’ Affiliations

(1)
Dipartimento di Matematica, Universitá di Cagliari

References

  1. Andersson L, Chruściel PT: Solutions of the constraint equations in general relativity satisfying "hyperboloidal boundary conditions". Dissertationes Mathematicae (Rozprawy Matematyczne) 1996, 355: 1-100.MathSciNetMATHGoogle Scholar
  2. Anedda C, Buttu A, Porru G: Boundary estimates for blow-up solutions of elliptic equations with exponential growth. to appear in Proceedings Differential and Difference Equations
  3. Anedda C, Porru G: Higher order boundary estimates for blow-up solutions of elliptic equations. to appear in Differential Integral Equations
  4. Bandle C: Asymptotic behaviour of large solutions of quasilinear elliptic problems. Zeitschrift für Angewandte Mathematik und Physik 2003,54(5):731-738. 10.1007/s00033-003-3207-0MathSciNetView ArticleMATHGoogle Scholar
  5. Bandle C, Giarrusso E: Boundary blow up for semilinear elliptic equations with nonlinear gradient terms. Advances in Differential Equations 1996,1(1):133-150.MathSciNetMATHGoogle Scholar
  6. Bandle C, Marcus M: "Large" solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behaviour. Journal d'Analyse Mathématique 1992, 58: 9-24.MathSciNetView ArticleMATHGoogle Scholar
  7. Bandle C, Marcus M: On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. Differential and Integral Equations 1998,11(1):23-34.MathSciNetMATHGoogle Scholar
  8. Bandle C, Marcus M: Dependence of blowup rate of large solutions of semilinear elliptic equations, on the curvature of the boundary. Complex Variables. Theory and Application 2004,49(7–9):555-570.MathSciNetView ArticleMATHGoogle Scholar
  9. Berhanu S, Porru G: Qualitative and quantitative estimates for large solutions to semilinear equations. Communications in Applied Analysis 2000,4(1):121-131.MathSciNetMATHGoogle Scholar
  10. Bieberbach L: und die automorphen Funktionen. Mathematische Annalen 1916,77(2):173-212. 10.1007/BF01456901MathSciNetView ArticleGoogle Scholar
  11. del Pino M, Letelier R: The influence of domain geometry in boundary blow-up elliptic problems. Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2002,48(6):897-904.MathSciNetView ArticleMATHGoogle Scholar
  12. Gilbarg D, Trudinger NS: Elliptic Partial Differential Equations of Second Order, Grundlehren der mathematischen Wissenschaften. Volume 224. Springer, Berlin; 1977:x+401.View ArticleGoogle Scholar
  13. Greco A, Porru G: Asymptotic estimates and convexity of large solutions to semilinear elliptic equations. Differential and Integral Equations 1997,10(2):219-229.MathSciNetMATHGoogle Scholar
  14. Keller JB:On solutions of . Communications on Pure and Applied Mathematics 1957, 10: 503-510. 10.1002/cpa.3160100402MathSciNetView ArticleMATHGoogle Scholar
  15. Lazer AC, McKenna PJ: Asymptotic behavior of solutions of boundary blowup problems. Differential and Integral Equations 1994,7(3-4):1001-1019.MathSciNetMATHGoogle Scholar
  16. Osserman R:On the inequality . Pacific Journal of Mathematics 1957,7(4):1641-1647.MathSciNetView ArticleMATHGoogle Scholar

Copyright

© Anedda et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.