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

Silvestre, Luis; Cardaliaguet, Pierre

Silvestre, Luis; Cardaliaguet, Pierre (2012), Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side, Communications in Partial Differential Equations, 37, 9, p. 1668-1688. http://dx.doi.org/10.1080/03605302.2012.660267

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00633218/fr/

Date

2012

Journal name

Communications in Partial Differential Equations

Volume

Number

Publisher

Springer

Pages

1668-1688

Abstract (EN)

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.

Subjects / Keywords

superquadratic growth; Hölder continuity; Hamilton-Jacobi equations