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Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a sub-spherical sector. (English) Zbl 1467.35173

Summary: The paper is devoted to the qualitative properties of positive solutions to a semilinear elliptic equation in a planar sub-spherical sector. Under certain range of amplitudes, we prove some monotonicity properties via the method of moving planes. The symmetry properties follow from the uniqueness of the corresponding over-determined problem by A. Farina and E. Valdinoci [Am. J. Math. 135, No. 6, 1699–1726 (2013; Zbl 1312.35138)].

MSC:

35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J25 Boundary value problems for second-order elliptic equations
35B09 Positive solutions to PDEs
35B06 Symmetries, invariants, etc. in context of PDEs

Citations:

Zbl 1312.35138
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Full Text: DOI

References:

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