Local Regularity And Local Boundedness For Weak Solutions Of Antisotropic Obstacle Problems

A-harmonic equation is an important kind of quasilinear ellipitc equation. The local regularity and the local boundedness for weak solution of A-harmonic equation is the classical results for the thoery of A-harmonic equation. This thesis mainly studies the properties for weak solutions of A-harmonic equation. This dissertation focuses on two sides:one is the local regularity for weak solutions ofΚψ,θqi-obstacle problems to the homogeneous equation, the other is the local boundedness for weak solutions ofΚψ,0qi-obstacle problems to the non-homogeneous equation. By means of changing some conditions that satisfies the equation appropriately, we proved the local regularity and the local boundedness for weak solution of A-harmonic equation by using a special kind of Sobolev inequality, constructing a test function and combining with some basic inequalities.