A priori estimates for a class of quasi-linear elliptic equations
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- by Daniel Daners and Pavel Drábek PDF
- Trans. Amer. Math. Soc. 361 (2009), 6475-6500 Request permission
Abstract:
In this paper we prove a priori estimates for a class of quasi-linear elliptic equations. To make the proofs clear and transparent we concentrate on the $p$-Laplacian. We focus on $L_p$-estimates for weak solutions of the problem with all standard boundary conditions on non-smooth domains. As an application we prove existence, continuity and compactness of the resolvent operator. We finally prove estimates for solutions to equations with non-linear source and show that, under suitable growth conditions, all solutions are globally bounded.References
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Additional Information
- Daniel Daners
- Affiliation: School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia
- MR Author ID: 325132
- ORCID: 0000-0002-0122-3789
- Email: D.Daners@maths.usyd.edu.au
- Pavel Drábek
- Affiliation: Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic
- Email: pdrabek@kma.zcu.cz
- Received by editor(s): November 2, 2007
- Published electronically: July 20, 2009
- Additional Notes: The second author was supported by Research Plan MSM4977751301 of the Czech Ministry of Education, Youths and Sports
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 6475-6500
- MSC (2000): Primary 35B45, 35B65, 35J65, 35J70
- DOI: https://doi.org/10.1090/S0002-9947-09-04839-9
- MathSciNet review: 2538601