Abstract We derive the weakly coupled systems of the infinity Laplace equations via a tug-of-war game introduced by Peres, Schramm, Sheffield, and Wilson (2009). We establish existence, uniqueness ...

We study the inhomogeneous infinity Laplace equation and prove that for bounded and continuous inhomogeneities, any blow-up is linear but not necessarily unique. If, in addition, the inhomogeneity is ...

The infinity Laplacian, a highly degenerate elliptic operator formally defined by Δ∞u = uₓᵢ uₓⱼ uₓᵢₓⱼ, has emerged as a central object in the study of L∞ variational problems and optimal Lipschitz ...

When mathematician Georg Cantor first glimpsed the true nature of infinity, it changed mathematics forever. He demonstrated that infinity isn’t just endless—it exists in different sizes, each opening ...

NOVA: How do mathematicians define infinity? Netz: Something which is equal to some of its parts. That's really the technical definition. NOVA: Is there a difference between the mathematical concept ...

A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA It can be easy to take math for granted. But ...