The Regularity For Weak Solutions Of A Class Of Elliptic Equations

In the theoretical research of elliptic partial differential equations,the regularity of the equations is one of the main research contents.As a very important category of elliptic partial differential equations,A-harmonic equations are widely used in mathematics,physics,mechanics,and engineering technology.Therefore,the research on the regularity of the solution of this type of equation has both theoretical significance and application value.The article mainly studies the regularity of weak solutions of a class of elliptic equations,and the details are as follows:1.The boundary value problem of non homogeneous p-harmonic equations.The Hodge decomposition method is used to construct a suitable test function,and through the Stampacchia lemma to construct the global regularity of the weak solution to the boundary value problem of the equation.2.The gradient estimates of weak solutions of non-homogeneous A-harmonic equations with variable exponents.The maximum function method is used to obtain the corresponding conclusions.3.The gradient estimation of the weak solution to obstacle problems for the nonhomogeneous A-harmonic equation.The iterative covering approximation method is used to get the corresponding conclusions.Figure 0;Table 0;Reference 52...