Regularity for an anisotropic equation in the plane

Abstract

We present a simple proof of the $C^1$ regularity of $p$-anisotropic functions in the plane for $2\le p<\infty$. We achieve a logarithmic modulus of continuity for the derivatives. The monotonicity (in the sense of Lebesgue) of the derivatives is used. The case with two exponents is also included.

9 pages