论文标题
小数dirichlet sublinear型问题的小订单极限
Small order limit of fractional Dirichlet sublinear-type problems
论文作者
论文摘要
我们研究了分数参数倾向于零时，解决各种dirichlet sublinear型问题的解决方案的渐近行为涉及分数拉普拉斯式。根据非线性的类型，正面解决方案可以根据对数laplacian（即具有傅立叶符号$ \ ln（|ξ| ement）$的pseudoDivferential Operator（| ementifferential Opitiator）融合到特征函数或极限非线性问题的阳性解决方案。在物流型非线性的情况下，我们的结果具有以下生物学解释：在存在有毒边界的情况下，迁移率降低的物种的饱和度阈值较低，存活率较高，并且分布更均匀。由于独立的兴趣，我们表明透明的对数问题具有独特的最小能源解决方案，该解决方案是有界的，并且与log-hölder连续模量连续连续。
We study the asymptotic behavior of solutions to various Dirichlet sublinear-type problems involving the fractional Laplacian when the fractional parameter s tends to zero. Depending on the type on nonlinearity, positive solutions may converge to a characteristic function or to a positive solution of a limit nonlinear problem in terms of the logarithmic Laplacian, that is, the pseudodifferential operator with Fourier symbol $\ln(|ξ|^2)$. In the case of a logistic-type nonlinearity, our results have the following biological interpretation: in the presence of a toxic boundary, species with reduced mobility have a lower saturation threshold, higher survival rate, and are more homogeneously distributed. As a result of independent interest, we show that sublinear logarithmic problems have a unique least-energy solution, which is bounded and Dini continuous with a log-Hölder modulus of continuity.
