Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian
HTML articles powered by AMS MathViewer

by Andrea Dall’Aglio and Alessio Porretta PDF
Trans. Amer. Math. Soc. 367 (2015), 3017-3039 Request permission

Abstract:

In this paper, we study the regularity of weak solutions and subsolutions of second order elliptic equations having a gradient-dependent term with superquadratic growth. We show that, under appropriate integrability conditions on the data, all weak subsolutions in a bounded and regular open set $\Omega$ are Hölder-continuous up to the boundary of $\Omega$. Some local and global summability results are also presented. The main feature of this kind of problem is that the gradient term, not the principal part of the operator, is responsible for the regularity.
References
Similar Articles
Additional Information
  • Andrea Dall’Aglio
  • Affiliation: Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5 - 00185 Roma, Italy
  • Email: dallaglio@mat.uniroma1.it
  • Alessio Porretta
  • Affiliation: Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica - 00133 Roma, Italy
  • MR Author ID: 631455
  • Email: porretta@mat.uniroma2.it
  • Received by editor(s): May 7, 2012
  • Received by editor(s) in revised form: October 4, 2012
  • Published electronically: January 15, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 3017-3039
  • MSC (2010): Primary 35B65, 35J60; Secondary 35R45, 35R05
  • DOI: https://doi.org/10.1090/S0002-9947-2015-05976-5
  • MathSciNet review: 3314800