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

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
37
Number
9
Publisher
Springer
Pages
1668-1688
Publication identifier
http://dx.doi.org/10.1080/03605302.2012.660267
Metadata
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Author(s)
Silvestre, Luis
Cardaliaguet, Pierre
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

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