论文标题
对一般准线性椭圆方程的非常弱的解决方案的梯度估计值
Gradient estimates of very weak solutions to general quasilinear elliptic equations
论文作者
论文摘要
我们为具有非标准生长条件的准椭圆方程的非常弱的解决方案建立了梯度估计，这是$ p $ laplace方程的自然概括。我们研究了梯度估计值的最大程度，而没有对基本结构假设以外的非线性进行任何规律性假设。我们的结果还包括梯度的较高的整合性结果以及对此类非线性问题非常弱的解决方案的存在。
We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the $p$-Laplace equation. We investigate the maximum extent for the gradient estimate to hold without imposing any regularity assumption on the nonlinearity other than basic structure assumptions. Our results also include a higher integrability result of the gradient and the existence for the very weak solutions to such nonlinear problems.
