By Braides A., Malchiodi A.
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PARTIAL SYMMETRIES A N D S Y M M E T R I C SETS OF SOLUTIONS TO PDE'S GIAMPAOLO CICOGNA Dip. it sez. e. of sets which are mapped into themselves by the symmetry. We introduce the definition of partial symmetry, which in some sense generalizes the concept of conditional symmetry, and show that the above notions may be preserved, although the symmetry is not exact. Some simple examples are also considered. 1. I n t r o d u c t i o n The usefulness of the notion of symmetry of a differential equation certainly does not need to be emphasized, both for its applications in the abstract analysis, and for the very concrete aim of finding explicit solutions (see 1 - u and references therein); but probably the most obvious and direct consequence is the fact that any symmetry of a given equation transforms solutions into (generally, different) solutions of the same equation.
Curvature theory of boundary phases the two-dimensional case by Braides A., Malchiodi A.