Abstract
The stability with respect top of the non-linear eigenvalue problem div(|∇u|p−2∇u)+λ|u|p−2 u=0 is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, R.:Sobolev Spaces, Academic Press, New York (1975).
Dibenedetto, E.:C 1+α local regularity of weak solutions of degenerate elliptic equations.Nonlinear Analysis TMA 7 (1983), 827–859.
Esteban, J. and Vazquez, J.: Homogeneous diffusion inR with power-like nonlinear diffusivity.Archive for Rational Mechanics and Analysis 103 (1988), 39–80.
Gilbarg, D. and Trudinger, N.:Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer-Verlag, Berlin (1983).
Gariepy, R. and Ziemer, W.: A regularity condition at the boundary for solutions of quasilinear elliptic equations,Arch. Rat. Mech. Anal. 67 (1977), 25–89.
Hedberg, L. and Wolff, Th.: Thin sets in nonlinear potential theory,Ann. Inst. Fourier (Grenoble) 33 (1983), 161–187.
Lindqvist, P.: Stability for the solutions of div(|∇u|p−2∇u)=f with varyingp, Journal of Mathematical Analysis and Applications 127 (1987), 93–102.
Lindqvist, P.: On the equation div(|∇u|p−2∇u)+λ|u|p−2 u=0,Proceedings of the American Mathematical Society 109 (1990), 157–164. Addendum,ibid. 116 (1992), 583–584.
Ladyzhenskaya, O. and Ural'tseva, N.:Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
Martio, O.: Capacity and measure densities,Annales Academiae Scientiarum Fennicae, Series A. I. Mathematica 4 (1978/1979), 109–118.
Maz'ya, V.: On the continuity at a boundary point of solutions of quasi-linear elliptic equations,Vestnik Leningradskogo Universiteta 25 (1970), 42–55 (in Russian),Vestnik Leningrad Univ. Math. 3 (1976), 225–242 (English translation).
Maz'ja, V.:Sobolev Spaces, Springer-Verlag, Berlin (1985).
Nevanlinna, R.: Über die Kapazität der Cantorschen Punktmengen,Monatshefte für Mathematik und Physik 43 (1936), 435–447.
Ohtsuka, M.: Capasité d'ensembles de Cantor généralisés,Nagoya Mathematical Journal 11 (1957), 141–160.
Pólya, G. and Szegö, G.:Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton (1951).
Sakaguchi, S.: Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems,Annali della Scuola Normale Superiore de Pisa, Serie IV (Classe de Scienze) 14 (1987), 403–421.
de Thélin, F.: Quelques résultats d'existence et de non-existence pour une E.D.P. elliptique non linéaire,C.R. Acad. Sc. Paris, Série I 299 (1984), 911–914.
de Thélin, F.: Sur l'espace propre associé à la première valeur propre du pseudo-laplacien,C.R. Acad. Sc. Paris, Série I 303 (1986), 355–358.
Tolksdorf, P.: Regularity for a more general class of quasi-linear elliptic equations,Journal of Differential Equations 51 (1984), 126–150.
Trudinger, N.: On Harnack type inequalities and their application to quasilinear elliptic equations,Communications on Pure and Applied Mathematics 20 (1967), 721–747.
Wiener, N.: The Dirichlet problem,Journal of Math. and Phys., Massachusetts Institute of Technology 3 (1924), 127–146.
Ziemer, W.:Weakly Differentiable Functions (Sobolev Spaces and Functions of Bounded Variation), Springer-Verlag, New York (1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lindqvist, P. On Non-Linear Rayleigh quotients. Potential Anal 2, 199–218 (1993). https://doi.org/10.1007/BF01048505
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01048505