Regularity for the normalized <i>p</i> -Laplacian equation with an arbitrary degeneracy law

Abstract We examine the interior regularity of solutions to a degenerate normalized p -Laplace equation, where the degeneracy is governed by a modulus of continuity whose inverse satisfies a Dini continuity condition. We prove that under very general assumptions on the degeneracy law, solutions belong to the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>C</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> {C^{1}} class. We argue by approximating the solutions by a sequence of hyperplanes, which allows us to prove the desired regularity.