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Symmetry results for elliptic Schrödinger systems on half spaces. (English) Zbl 1260.35162

Summary: In this paper, we prove some symmetry and monotonicity results for classical positive solutions for elliptic Schrödinger systems on half spaces with the Neumann type condition. Our methods employ the Alexandrov-Serrin method of moving planes combined with Hopf’s lemma at a corner.

MSC:

35Q41 Time-dependent Schrödinger equations and Dirac equations
35J10 Schrödinger operator, Schrödinger equation
35B09 Positive solutions to PDEs
35B06 Symmetries, invariants, etc. in context of PDEs
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