【摘要】 讨论了Ｒｎ（ｎ≥２）中有界开集Ω上二阶拟线性椭圆型方程Ｄｉｒｉｃｈｌｅｔ边值问题很弱解的　边界正则性，其中Ω边界为Ｌｉｐｓｃｈｉｔｚ边界．采用Ｈｏｄｇｅ分解的方法建立适当的检　验函数，对Ｄｉｒｉｃｈｌｅｔ问题很弱解得到了逆Ｈｌｄｅｒ不等式，改进了很弱解梯度的可积性，使　其成为经典意义下的弱解．更多还原

【Abstract】 Boundary higher integrability for the gradient of very weak solutions u(x)∈W1,r(Ω) to the Dirichlet bounda ry value problem for a second order quasilinear elliptic type equation is discus sed on bounded open set ΩRn,where the bound Ω is Lipschitz.Here Hodge decomposition is used to construct a suitable test function, the reverse H lder inequality for very weak solutions of Dirichlet problem is proved.Thus th e integrability for the gradient of very weak solution u(x) is improved,u(x) is a weak solution in usual sense.更多还原