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June 2009 Reflection principle for quasiminimizers
Olli Martio
Funct. Approx. Comment. Math. 40(2): 165-173 (June 2009). DOI: 10.7169/facm/1246454026

Abstract

It is shown that the reflection principle holds for $K$--quasiminimizers in $\mathbb{R}^n$, $n \geq 2$, provided that $K \in [1, 2)$. For $n = 1$ the principle holds for all $K \geq 1$ and an example shows that $K$ is not preserved in the reflection process. A local integrability result up to the boundary is proved for the derivative of a quasiminimizer in $\mathbb{R}^n$, $n \geq 1$; the result is needed for the reflection principle.

Citation

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Olli Martio. "Reflection principle for quasiminimizers." Funct. Approx. Comment. Math. 40 (2) 165 - 173, June 2009. https://doi.org/10.7169/facm/1246454026

Information

Published: June 2009
First available in Project Euclid: 1 July 2009

zbMATH: 1183.31003
MathSciNet: MR2543554
Digital Object Identifier: 10.7169/facm/1246454026

Subjects:
Primary: 31B25
Secondary: 35J65

Rights: Copyright © 2009 Adam Mickiewicz University

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Vol.40 • No. 2 • June 2009
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