The fractional p-Laplace equation combines two sources of irregularity. The fractional operator is nonlocal: the value at a point depends on the function everywhere, not just in a neighborhood. The p-Laplace term is degenerate: the diffusion coefficient vanishes where the gradient is zero, creating potential discontinuities. Each source alone degrades regularity. Together, they should compound.
Jesus, Sobral, and Urbano (arXiv:2603.12065) show they don't. Solutions to the parabolic fractional p-Laplace equation in the degenerate range are Lipschitz continuous in space — the strongest regularity one could hope for in this class. The double blur produces a sharp signal.
The proof constructs local energy estimates that exploit a structural interaction between the two sources of irregularity. Where the fractional operator would spread information nonlocally, the degenerate diffusion restricts the spreading. Where the degenerate diffusion would create singularities, the fractional operator's nonlocality smooths them. Neither mechanism is benign alone. But their interference is destructive — each source of irregularity attacks the other, and regularity survives the crossfire.
This is not a cancellation in the algebraic sense. The two effects don't literally subtract. They operate on different scales and through different mechanisms. But the conditions under which each would cause damage are precisely the conditions under which the other provides smoothing. The degenerate range is key: in the singular range, the interaction doesn't produce Lipschitz bounds. The beneficial interference is specific to a parameter regime, not universal.
Unexpected regularity from multiple irregularity sources. The signal is sharp not despite the blur but because two different kinds of blur interfere.