- Volume 32 Issue 4
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UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY
- Lee, Yong Hah (Department of Mathematics Education Ewha Womans University)
- Received : 2016.11.07
- Accepted : 2017.02.02
- Published : 2017.10.31
We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.
Supported by : National Research Foundation of Korea(NRF)
- J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry 6 (1971), 119-128. https://doi.org/10.4310/jdg/1214430220
- E. Hewitt and K. Stormberg, Real and Abstract Analysis, Springer-Verlag, New York, Heidelberg, Berlin, 1965.
- Y. H. Lee, Rough isometry and energy finite solutions of elliptic equations on Riemannian manifolds, Math. Ann. 318 (2000), no. 1, 181-204. https://doi.org/10.1007/s002080000118
- Y. H. Lee, Rough isometry and p-harmonic boundaries of complete Riemannian manifolds, Potential Anal. 23 (2005), no.1, 83-97. https://doi.org/10.1007/s11118-004-3261-z
- J. Maly and W. P. Ziemer, Fine regularity of solutions of elliptic partial differential equations, Mathematical Surveys and Monographs, 51. American Mathematical Society, Providence, RI, 1997.
- L. Sario and M. Nakai, Classification Theory of Riemann Surfaces, Springer Verlag, Berlin, Heidelberg, New York, 1970.