Everywhere differentiability of absolute minimizers for locally strongly convex and concave Hamiltonian $H(p)\in C^0({\mathbb{R}}^n)$ with $n\ge 3$

Abstract

Suppose that $n\ge 3$ and $H(p)\in C^0({\mathbb{R}}^n)$ is a locally strongly convex and concave Hamiltonian. We obtain the everywhere differentiability of all absolute minimizers for $H$ in any domain of ${\mathbb{R}}^n$.

21 pages

References in corpus (2)

• Regularity of absolute minimizers for continuous convex Hamiltonians
• A quantative Sobolev regularity for absolute minimizers involving Hamiltonian $H(p)\in C^0({\mathbb{R}}^2)$ in plane