Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian


Authors: Andrea Dall’Aglio and Alessio Porretta
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
Published electronically: January 15, 2015
MathSciNet review: 3314800
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 35B65, 35J60, 35R45, 35R05

Retrieve articles in all journals with MSC (2010): 35B65, 35J60, 35R45, 35R05


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
Email: porretta@mat.uniroma2.it

DOI: https://doi.org/10.1090/S0002-9947-2015-05976-5
Keywords: Elliptic equations, superquadratic growth, H\"older continuity of solutions, local estimates, boundedness of solutions
Received by editor(s): May 7, 2012
Received by editor(s) in revised form: October 4, 2012
Published electronically: January 15, 2015
Article copyright: © Copyright 2015 American Mathematical Society