Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 36, 2011, 301-319

POWER-TYPE QUASIMINIMIZERS

Anders Björn and Jana Björn

Linköping University, Department of Mathematics
SE-581 83 Linköping, Sweden; anbjo 'at' mai.liu.se

Linköping University, Department of Mathematics
SE-581 83 Linköping, Sweden; jabjo 'at' mai.liu.se

Abstract. In this paper we examine the quasiminimizing properties of radial power-type functions u(x) = |x|^\alpha in Rⁿ. We find the optimal quasiminimizing constant whenever u is a quasiminimizer of the p-Dirichlet integral, p \neq n, and similar results when u is a quasisub- and quasisuperminimizer. We also obtain similar results for log-powers when p = n.

2000 Mathematics Subject Classification: Primary 49J20; Secondary 31C45, 35J20.

Key words: Doubling measure, nonlinear, p-harmonic, Poincaré inequality, potential theory, quasiminimizer, quasisubharmonic, quasisubminimizer, quasisuperharmonic, quasisuperminimizer.

Reference to this article: A. Björn and J. Björn: Power-type quasiminimizers. Ann. Acad. Sci. Fenn. Math. 36 (2011), 301-319.

Full document as PDF file

doi:10.5186/aasfm.2011.3619