Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 215-225

THE QUASISUPERMINIMIZING CONSTANT FOR THE MINIMUM OF TWO QUASISUPERMINIMIZERS IN Rⁿ

Anders Björn, Jana Björn and Ismail Mirumbe

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

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

Makerere University, Department of Mathematics
P.O. Box 7062, Kampala, Uganda; mirumbe 'at' cns.mak.ac.ug

Abstract. It was shown in Björn–Björn–Korte [5] that u := min{u₁,u₂} is a ‾Q-quasisuperminimizer if u₁ and u₂ are Q-quasisuperminimizers and ‾Q = 2Q²/(Q + 1). Moreover, one-dimensional examples therein show that ‾Q is close to optimal. In this paper we give similar examples in higher dimensions. The case when u₁ and u₂ have different quasisuperminimizing constants is considered as well.

2010 Mathematics Subject Classification: Primary 31C45; Secondary 35J60.

Key words: Nonlinear potential theory, quasiminimizer, quasisuperminimizer.

Reference to this article: A. Björn, J. Björn and I. Mirumbe: The quasisuperminimizing constant for the minimum of two quasisuperminimizers in Rⁿ. Ann. Acad. Sci. Fenn. Math. 45 (2020), 215-225.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4508

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