Lee, Yong Hah Uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators via \(p\)-harmonic boundary. (English) Zbl 1383.58010 Commun. Korean Math. Soc. 32, No. 4, 1025-1031 (2017). Summary: 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 \(f\). MSC: 58J05 Elliptic equations on manifolds, general theory 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions Keywords:\(\mathcal{A}\)-harmonic function; \(p\)-harmonic boundary; boundary value problem PDFBibTeX XMLCite \textit{Y. H. Lee}, Commun. Korean Math. Soc. 32, No. 4, 1025--1031 (2017; Zbl 1383.58010) Full Text: DOI References: [1] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Riccicurvature, J. Differential Geometry 6 (1971), 119-128. · Zbl 0223.53033 [2] E. Hewitt and K. Stormberg, Real and Abstract Analysis, Springer-Verlag, New York,Heidelberg, Berlin, 1965. [3] Y. H. Lee, Rough isometry and energy finite solutions of elliptic equations on Riemannianmanifolds, Math. Ann. 318 (2000), no. 1, 181-204. · Zbl 0968.58018 [4] , Rough isometry and p-harmonic boundaries of complete Riemannian manifolds,Potential Anal. 23 (2005), no.1, 83-97. · Zbl 1082.31005 [5] J. Mal´y and W. P. Ziemer, Fine regularity of solutions of elliptic partial differentialequations, Mathematical Surveys and Monographs, 51. American Mathematical Society,Providence, RI, 1997. [6] L. Sario and M. Nakai, Classification Theory of Riemann Surfaces, Springer Verlag,Berlin, Heidelberg, New York, 1970.Yong Hah LeeDepartment of Mathematics EducationEwha Womans UniversitySeoul 120-750, KoreaE-mail address: yonghah@ewha.ac.kr · Zbl 0199.40603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.