# UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY

• Lee, Yong Hah
• Accepted : 2017.02.02
• Published : 2017.10.31
• 30 2

#### Abstract

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.

#### Keywords

${\mathcal{A}}$-harmonic function;p-harmonic boundary;boundary value problem

#### References

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#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)