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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hölder estimates for degenerate elliptic equations with coercive Hamiltonians


Authors: I. Capuzzo Dolcetta, F. Leoni and A. Porretta
Journal: Trans. Amer. Math. Soc. 362 (2010), 4511-4536
MSC (2010): Primary 35J70, 35B65
Published electronically: April 14, 2010
MathSciNet review: 2645039
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Abstract: We prove a priori estimates and regularity results for some quasilinear degenerate elliptic equations arising in optimal stochastic control problems. Our main results show that strong coerciveness of gradient terms forces bounded viscosity subsolutions to be globally Hölder continuous, and solutions to be locally Lipschitz continuous. We also give an existence result for the associated Dirichlet problem.


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Additional Information

I. Capuzzo Dolcetta
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro 2, 00185 Roma, Italy
Email: capuzzo@mat.uniroma1.it

F. Leoni
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro 2, 00185 Roma, Italy
Email: leoni@mat.uniroma1.it

A. Porretta
Affiliation: Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Email: porretta@mat.uniroma2.it

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04807-5
PII: S 0002-9947(10)04807-5
Keywords: Degenerate elliptic equations, coercive Hamiltonians, H\"older regularity, viscosity (sub)solutions
Received by editor(s): January 28, 2008
Published electronically: April 14, 2010
Additional Notes: This work was partially supported by PRIN-COFIN 2005 Project “Viscosity, metric and control theoretic methods in nonlinear partial differential equations”
Article copyright: © Copyright 2010 American Mathematical Society