Reflection principle for quasiminimizers

Martio, Olli

Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, p. 165-173 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2009-06-15
Classification:  quasilinear elliptic equation,  reflection principle,  the Sobolev space,  quasiminimizer,  31B25,  35J65