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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 $f$.
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참고문헌 (6)
참고문헌 신청
E. Hewitt / 1965 / Real and Abstract Analysis / Springer-Verlag
J. Cheeger / 1971 / The splitting theorem for manifolds of nonnegative Ricci curvature / J. Differential Geometry 6 : 119 ~ 128
J. Maly / 1997 / Fine regularity of solutions of elliptic partial differential equations / American Mathematical Society
L. Sario / 1970 / Classification Theory of Riemann Surfaces / Springer Verlag
Y. H. Lee / 2000 / Rough isometry and energy finite solutions of elliptic equations on Riemannian manifolds / Math. Ann. 318 (1) : 181 ~ 204
J. Cheeger / 1971 / The splitting theorem for manifolds of nonnegative Ricci curvature / J. Differential Geometry 6 : 119 ~ 128
J. Maly / 1997 / Fine regularity of solutions of elliptic partial differential equations / American Mathematical Society
L. Sario / 1970 / Classification Theory of Riemann Surfaces / Springer Verlag
Y. H. Lee / 2000 / Rough isometry and energy finite solutions of elliptic equations on Riemannian manifolds / Math. Ann. 318 (1) : 181 ~ 204
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