论文标题
一类非线性分数拉普拉斯和单数问题的规律性结果
Regularity results for a class of nonlinear fractional Laplacian and singular problems
论文作者
论文摘要
在本文中，我们研究了$（p）$（p）$（请参阅下）的弱解决方案的存在，唯一性，不存在和规律性，涉及平滑有限域中的奇异非线性和奇异权重。我们通过近似方法证明了$ w_ {loc}^{s，p}（ω）$中的弱解决方案的存在。建立一个新的独立兴趣的新比较原则，我们证明了弱解决方案的独特性，价格为$ 0 \leqΔ<1+s- \ frac {1} {p} {p} $，并且进一步，$Δ\ geq sp。$Δ\ geqsp。的弱解决方案不存在，$ $ $ $ $Δ因此，我们证明了Hölder的规律性，直到边界和最佳sobolev规律性，以最小的弱解决方案。
In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type $(P)$ (see below) involving singular nonlinearity and singular weights in smooth bounded domain. We prove the existence of weak solution in $W_{loc}^{s,p}(Ω)$ via approximation method. Establishing a new comparison principle of independent interest, we prove the uniqueness of weak solution for $0 \leq δ< 1+s- \frac{1}{p}$ and furthermore the nonexistence of weak solution for $δ\geq sp.$ Moreover, by virtue of barrier arguments we study the behavior of minimal weak solution in terms of distance function. Consequently, we prove Hölder regularity up to the boundary and optimal Sobolev regularity for minimal weak solutions.
