论文标题
非线性椭圆方程在Orlicz空间中的存在和规律性结果
Existence and regularity results for nonlinear elliptic equations in Orlicz spaces
论文作者
论文摘要
我们关注的是，对于由一般差分运算符驱动的一类准线性椭圆方程的解决方案的存在和规律性，具体取决于$（x，u，u，\ nabla u）$，以及对流$ f $。方程成员的假设是根据Young的功能提出的，因此我们在Orlicz-Sobolev空间中工作。在建立了一些辅助特性（在我们的上下文中似乎是新的）之后，我们提出了两个存在和两个规律性的结果。我们以几个例子结束。
We are concerned with the existence and regularity of the solutions to the Dirichlet problem, for a class of quasilinear elliptic equations driven by a general differential operator, depending on $(x,u,\nabla u)$, and with a convective term $f$. The assumptions on the members of the equation are formulated in terms of Young's functions, therefore we work in the Orlicz-Sobolev spaces. After establishing some auxiliary properties, that seem new in our context, we present two existence and two regularity results. We conclude with several examples.
