Symmetry and regularity of an optimization problem related to a nonlinear BVP

ANEDDA, CLAUDIA;CUCCU, FABRIZIO

2013-01-01

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Abstract

We consider the functional where uf is the unique nontrivial weak solution of the boundary-value problem where Ω ⊂ Rn is a bounded smooth domain. We prove a result of Steiner symmetry preservation and, if n = 2, we show the regularity of the level sets of minimizers.