C1–regularity for degenerate diffusion equations.

We prove that any solution of a degenerate elliptic PDE is of class C 1 provided the inverse of the equation's degeneracy law satisfies an integrability criterium, viz. σ − 1 ∈ L 1 (1 λ d λ). The proof is based upon the construction of a sequence of converging tangent hyperplanes that approximate u (x) , near x 0 , by an error of order o (| x − x 0 |). Explicit control of such hyperplanes is carried over through the construction, yielding universal estimates upon the C 1 –regularity of solutions. Among the main new ingredients required in the proof, we develop an alternative recursive algorithm for renormalization of approximating solutions. This new method is based on a technique tailored to prevent the sequence of degeneracy laws constructed through the process from being, itself, degenerate. [ABSTRACT FROM AUTHOR]