Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side

Abstract

We show that solutions of time-dependent degenerate parabolic equations with super-quadratic growth in the gradient variable and possibly unbounded right-hand side are locally ${\mathcal{C}}^{0,\alpha }$. Unlike the existing (and more involved) proofs for equations with bounded right-hand side, our arguments rely on constructions of sub- and supersolutions combined with improvement of oscillation techniques.

Cited by in corpus (1)

• Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian