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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Hölder estimates for degenerate elliptic equations with coercive Hamiltonians
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by I. Capuzzo Dolcetta, F. Leoni and A. Porretta PDF
Trans. Amer. Math. Soc. 362 (2010), 4511-4536 Request permission

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
  • MR Author ID: 631455
  • Email: porretta@mat.uniroma2.it
  • 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”
  • © Copyright 2010 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 4511-4536
  • MSC (2010): Primary 35J70, 35B65
  • DOI: https://doi.org/10.1090/S0002-9947-10-04807-5
  • MathSciNet review: 2645039