Xavier Lamy

Another regularizing property of the 2D eikonal equation

A weak solution of the two-dimensional eikonal equation amounts to a vector field m:Ω⊂R2→R2 such that |m|=1 a.e. and divm=0 in D′(Ω). It is known that, if m has some low regularity, e.g., continuous or W1/3,3, then m is automatically more regular: locally Lipschitz outside a loca...