Global Integrability For Weak Solutions Of The A-Harmonic Equation And Its Obstacle Problems

The properties of A-harmonic equation and its obstacle problems have extensive research value and application prospect.With the deepening of the research on Aharmonic equation,scholars at home and abroad have made some achievements in this direction.Through the investigation of many relevant conclusions,it can be seen that there is still a large space to study the properties of the weak solutions of the inhomogeneous A-harmonic equation and its obstacle problems.The main purpose is to study the global integrability for the weak solutions of inhomogeneous A-harmonic equations and its obstacle problems.The main content is as follows:1.The boundary value problem of inhomogeneous p-harmonic equations is discussed.By using decomposition theorem to construct proper test function,Sobolev embedding theorem and Stampacchia lemma,the global integrability of very weak solutions of boundary value problems is obtained.2.The obstacle problem of the A-harmonic equation with inhomogeneous term as divergence.By establishing the global inverse H?lder inequality,the global integrability of the weak solution to the obstacle problem is obtained by using the Gehring lemma.3.The obstacle problem of the A-harmonic equation with non-homogeneous term.By using the Hodge decomposition theorem to construct the appropriate admissible function,and by using the estimation tools such as Young inequality and H?lder inequality,the global inverse H?lder inequality is established,and the global integrability of the weak solutions of the obstacle problem is obtained.Figure 0;Table 0;Reference 51...