Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian
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- by Andrea Dall’Aglio and Alessio Porretta PDF
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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
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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