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Let V be a convex neighborhood of the origin contained in the square Q = {(x, y) ∈ R 2 : |x| ≤ π, |y| ≤ π }. Let A be a 'sector' of V bounded by two convex or concave curves intersecting at the origin. Let f be an integrable function on Q, smooth on A and on V \ A but having a jump discontinuity at the origin, whose coordinate sections (i. e., the restrictions of f to x = const, resp. y = const) have uniformly bounded variation. Under essentially these conditions the partial sums S n,n of the Fourier series of f display for n → ∞ at the origin a corner point Gibbs phenomenon with an overshoot of up to 37,4% of half the jump size. This Gibbs phenomenon manifests itself in the pointwise convergence of S n,n ( x n , y n ; f ) as n → ∞ for all (x, y) ∈ R 2 to a non-constant limiting function only depending on the slopes of the boundary curves of A at the origin and on the jump of f (x, y) as (x, y) approaches (0, 0) within A resp. V \ A.

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