| Abstract: |
| We consider semilinear elliptic problems with mixed boundary conditions in spherical sectors contained in an unbounded cone in $\mathbb{R^N}$ and address the question of the radial symmetry of the positive solutions. We present some results which show that the symmetry, as well as the break of symmetry depends on the kind of cones considered. This implies that a Gidas-Ni-Nirenberg type result does not hold in any spherical sectors. Similar results hold for the critical exponent Neumann problem in the whole cone. |
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