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In this paper, we obtain a priori estimates for the set of anti-symmetricsolutions to a fractional Laplacian equation in a bounded domain using ablowing-up and rescaling argument. In order to establish a contradiction topossible blow-ups, we apply a certain variation of the moving planes method inorder to prove a monotonicity result for the limit equation after rescaling.

A priori estimates for anti-symmetric solutions to a fractional Laplacian equation in a bounded domain