- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 676215, 8 pages
Regularity Result for Quasilinear Elliptic Systems with Super Quadratic Natural Growth Condition
1Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, Fujian 363000, China
2School of Mathematical Science, Xiamen University, Xiamen, Fujian 361005, China
Received 31 December 2012; Accepted 2 April 2013
Academic Editor: Paul Eloe
Copyright © 2013 Shuhong Chen and Zhong Tan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. Giaquinta and G. Modica, “Partial regularity of minimizers of quasiconvex integrals,” Annales de l'institut Henri Poincaré, vol. 3, pp. 185–208, 1986.
- M. Giaquinta, “A counter-example to the boundary regularity of solutions to elliptic quasilinear systems,” Manuscripta Mathematica, vol. 24, no. 2, pp. 217–220, 1978.
- E. Giusti and M. Miranda, “Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari,” Archive for Rational Mechanics and Analysis, vol. 31, no. 3, pp. 173–184, 1968.
- A. A. Arkhipova, “Regularity results for quasilinear elliptic systems with nonlinear boundary conditions,” Journal of Mathematical Sciences, vol. 77, no. 4, pp. 3277–3294, 1995.
- A. A. Arkhipova, “On the regularity of solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearity,” Journal of Mathematical Sciences, vol. 80, no. 6, pp. 2208–2225, 1996.
- A. A. Arkhipova, “On the regularity of the oblique derivative problem for quasilinear elliptic systems,” Journal of Mathematical Sciences, vol. 84, no. 1, pp. 817–822, 1997.
- M. Wiegner, “A-Priori Schranken für Lösungen gewisser elliptischer Systeme,” Manuscripta Mathematica, vol. 18, no. 3, pp. 279–297, 1976.
- S. Hildebrandt and K. O. Widman, “On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order,” Annali della Scuola Normale Superiore di Pisa IV, vol. 4, pp. 144–178, 1977.
- J. Jost and M. Meier, “Boundary regularity for minima of certain quadratic functionals,” Mathematische Annalen, vol. 262, no. 4, pp. 549–561, 1983.
- F. Duzaar, J. Kristensen, and G. Mingione, “The existence of regular boundary points for non-linear elliptic systems: to the memory of Sergio Campanato,” Journal fur die Reine und Angewandte Mathematik, vol. 2007, no. 602, pp. 17–58, 2007.
- J. Kristensen and G. Mingione, “Boundary regularity in variational problems,” Archive for Rational Mechanics and Analysis, vol. 198, no. 2, pp. 369–455, 2010.
- S. Hildebrandt, “Nonlinear elliptic systems and harmonic mappings,” in Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, vol. 1, pp. 481–615, Science Press, Beijing, China, 1982, See also: Vorlesungsreihe 3, SFB 72, UniversitÄat, Bonn, Germany, 1980.
- S. Hildebrandt, “Quasilinear elliptic systems in diagonal form,” in Systems of Nonlinear Partial Differential Equations, J. M. Ball, Ed., pp. 173–217, Proceedings of Nato Advanced Study Institute, Oxford, UK, 1983.
- J. F. Grotowski, “Boundary regularity for quasilinear elliptic systems,” Communications in Partial Differential Equations, vol. 27, no. 11-12, pp. 2491–2512, 2002.
- F. Duzaar and K. Steffen, “Optimal interior and boundary regularity for almost minimal currents to elliptic integrands,” Journal für die Reine und Angewandte Mathematik, vol. 546, pp. 73–138, 2002.
- F. Duzaar and J. F. Grotowski, “Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation,” Manuscripta Mathematica, vol. 103, no. 3, pp. 267–298, 2000.
- J. F. Grotowski, “Boundary regularity for nonlinear elliptic systems,” Calculus of Variations and Partial Differential Equations, vol. 15, no. 3, pp. 353–388, 2002.
- W. K. Allard, “On the first variation of a varifold,” Annals of Mathematics, vol. 95, pp. 225–254, 1972.
- M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, NJ, USA, 1983.
- S. Campanato, “Equazioni ellittiche del IIo ordine e spazi ,” Annali di Matematica Pura ed Applicata, vol. 69, no. 1, pp. 321–381, 1965.
- S. Campanato, “Proprietà di Hölderianità di alcune classi di funzioni,” Annali della Scuola Normale Superiore di Pisa Series III, vol. 17, pp. 175–188, 1963.