论文标题
分数非线性的椭圆边界价值问题
An elliptic boundary value problem with fractional nonlinearity
论文作者
论文摘要
我们研究了解决二阶椭圆边界值问题的解决方案的存在和唯一性，该问题包含应用于分数laplacian的功率非线性。我们检测到将存在与不存在的制度区分开的关键力量。对于存在结果，我们利用特定的加权Sobolev空间来补偿自然构建问题的边界奇点。
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the non-existence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate boundary singularities which are naturally built in the problem.
