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Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a super-spherical sector. (English) Zbl 1473.35247

Summary: In this paper we establish some symmetry results for positive solutions of semilinear elliptic equations with mixed boundary conditions. In particular, we show that the positive solution in a super-spherical sector must be symmetric. The monotonicity property is also proved. Our proof is based on the well-known moving plane methods.

MSC:

35J61 Semilinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B06 Symmetries, invariants, etc. in context of PDEs
35B09 Positive solutions to PDEs
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