MAXIMUM PRINCIPLE AND COMPARISON PRINCIPLE OF p-HARMONIC FUNCTIONS VIA p-HARMONIC BOUNDARY OF GRAPHS

Abstract

We prove the maximum principle and the comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of $p$-harmonic functions via $p$-harmonic boundary of graphs.

Keywords

• maximum principle;
• comparison principle;
• p-harmonic function;
• p-harmonic boundary;
• boundary value problem

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

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