Solving Method Of Two Harmonic Functions' Dirichlet Problem And Discussion Of Harmonic Functions' Extremum Principle

In this paper ,we firstly gave the expression of laplace operator under the cylindrical coordinates using variational principle. Then we infered two solving methods of two harmonic functions' Dirichlet problem . Thereafter, we proved the extremum principle by hopf lemma.The paper mainly consists of the following parts:Chapter one introduced some knowledge of harmonic functions.Chapter two gave the expression of laplace operator under the cylindricalcoordinates using variational principle. The expression isChapter three infered two solving methods of the following two problem (problem one and problem two) and compared them .Problem one: Dirichlet problem of circle (A is a constant)Problem two: boundary value problemexpresses ball coordinate)Chapter four proved the important property of harmonic functions which was called extremum principle.