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Boundary Value Problems for Nonlinear Elliptic Equations of Second Order in High Dimensional Domains
School of Mathematical Sciences, Peking University, Beijing, China
Uniformed Services University of the Health Sciences, Bethesda, USA
- 1 School of Mathematical Sciences, Peking University, Beijing, China
- 2 Uniformed Services University of the Health Sciences, Bethesda, USA
Applied Mathematics·Volume 04 (2013)·Pages 1651–1657·Published 8 November 2013·DOI10.4236/am.2013.412225
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Abstract
This paper mainly concerns oblique derivative problems for nonlinear nondivergent elliptic equations of second order with measurable coefficients in a multiply connected domain. Under certain condition, we derive a priori estimates of solutions. By using these estimates and the fixed-point theorem, we prove the existence of solutions.
Keywordsblique Derivative ProblemsNonlinear Elliptic EquationsHigh Dimensional Domains
- H. O. Codres, “über die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen,” Mathematische Annalen, Vol. 131, No. 3, 1956, pp. 278-312. http://dx.doi.org/10.1007/BF01342965
- Y. A. Alkhutov and I. T. Mamedov, “The First Boundary Value Problem for Nondivergence Second Order Parabolic Equations with Discontinuous Coefficients,” Mathematics of the USSR-Sbornik, Vol. 59, No. 2, 1988, pp. 471-495. http://dx.doi.org/10.1070/SM1988v059n02ABEH003147
- O. A. Ladyshenskaja and N. N. Uraltseva, “Linear and Quasilinear Elliptic Equations,” Academic Press, New York, 1968.
- G. C. Wen, Z. L. Xu and H. Y. Gao, “Boundary Value Problems for Nonlinear Elliptic Equations in High Dimensional Domains,” Research Information Ltd., Slough, 2004.
- G. C. Wen, D. Chen and Z. L. Xu, “Nonlinear Complex Analysis and Its Applications,” Science Press, Beijing, 2008.
- G. C. Wen, “Recent Progress in Theory and Applications of Modern Complex Analysis,” Science Press, Beijing, 2010.
- G. C. Wen and D. Chen, “Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order with Measurable Coefficients in High Dimensional Domains,” Nonlinear Sciences and Numerical Simulation, Vol. 10 No. 5, 2005, pp. 559-570. http://dx.doi.org/10.1016/j.cnsns.2003.04.002
- D. Chen and G. C. Wen, “Some Boundary Value Problems for Nonlinear Elliptic Systems of Second Order in High Dimensional Domains,” Proceedings of the 3rd International Conference on Boundary Value Problems, Integral Equations and Related Problems, World Scientific, Singapore, 2011, pp. 12-21.