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Original Articles

Hölder Continuity to Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient and Unbounded Right-hand Side

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Pages 1668-1688 | Received 17 Oct 2011, Accepted 03 Jan 2012, Published online: 21 Aug 2012
 

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.

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