Regularity For Very Weak Solutions To Obstacle Problems Of A-Harmonic Equation

As we all know,many problems in physics and dynamics can be reduced to partial differential equations.As a generalization of Laplace equation and p-Laplace equation,A-harmonic equation has a very important application in solving practical problems.The regularity of very weak solutions for obstacle problems of several forms of A-harmonic equations is discussed.1.Obstacle problems of A-harmonic equation under nonstandard growth.By using the inverse H(?)lder inequality and Gehring lemma,the high-order integrability of weak solutions to obstacle problems of is obtained.2.Obstacle problems for homogeneous A-harmonic equations.Under structural conditions,by using Hodge decomposition theorem of perturbed vector field and Stampacchia lemma,the global regularity of very weak solutions to obstacle problems is obtained.3.Obstacle problems for A-harmonic equation with non-divergence nonhomogeneous terms.By using Hodge decomposition theorem of perturbed vector field and Stampacchia lemma,the global regularity of very weak solutions to obstacle problems of equations is obtained.4.Double obstacle problems for A-harmonic equation with divergence nonhomogeneous terms.By using Hodge decomposition theorem of perturbed vector field and H(?)lder inequality,Young inequality and other tools,combined with Stampacchia lemma,the global regularity of very weak solutions to double obstacle problems is obtained.Figure 0;Table 0;Reference 55...