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 𝒞0, α. 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.
Mathematics Subject Classification:
Acknowledgment
Luis Silvestre was partially supported by the Sloan fellowship and NSF grants DMS-1065979 and DMS-1001629.
The article has been completed while the first author was visiting Chicago University. He thanks the institution for its hospitality.