Properties Of Solutions Of Equations Of A-harmonic Type And Higher Order Iterative Estimation Of Operators

In the practical engineering and physical problems,the object to be studied is often affected by multiple variables,so it is generally expressed as partial differential equations.In addition to being a broad and profound mathematics discipline in itself,the partial differential equation also plays an important role in the construction of physical models,such as the Wave equation,the Heat Conduction equation,the Schrodinger equation and so on.Driven by practice and application,nonlinear elliptic equation arises at the right moment,and occupies a prominent position in the development process of partial differential equations.It has become an important toolto study various classical problems in mathematical physics,and is also relatively mature compared with hyperbolic and parabolic equations.A-harmonic equation is an important generalization of Laplace equation,and also an important component of nonlinear elliptic equation.It has been widely used in many fields,such as conformal geometry,holomorphic dynamical system,electrostatic field,fluid mechanics,elasticity theory,nonlinear analysis and bit potential theory.In the course of many years of development,although the theory of A-harmonic equation has been constantly improved,the study of the properties of its solution has always been one of the directions of great interest to mathematical workers.This paper uses the theory of monotone operator to discuss the existence and uniqueness of weak solutions of an inhomogeneous A-harmonic equation.On this basis,we apply the operator weak convergence lemma and H(?)lder inequality to discuss the gradient estimation and the convergence of weak solutions of the double obstacle problem.The correlation estimation of the operator iteration of the A-harmonic equation solution on the differential form is also studied.The Jensen inequality,Young inequality,Young equation,are applied to Orlicz space to obtain the local estimation of related operators,and the Whithey coverage theorem is applied to obtain the global estimate of the operator.