论文标题
分数半线性方程的稳定解决方案：唯一性，分类和近似结果
Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results
论文作者
论文摘要
我们研究了分数半线性方程的稳定解决方案$（-Δ）^s u = f（u）$ in $ω\ subset \ subset \ mathbb {r}^n $，用于凸出非线性$ f $，在dirichlet外部条件下我们建立了唯一性和分类结果，我们表明弱（能量）稳定的溶液可以通过一系列有界（正常）稳定的解决方案近似于类似问题。 作为结果的应用，我们确定了弱（能量）稳定解决方案的内部规律性，以解决半拉普拉斯的尺寸$ 1 \ leq n \ leq 4 $。
We study stable solutions to fractional semilinear equations $(-Δ)^s u = f(u)$ in $Ω\subset \mathbb{R}^n$, for convex nonlinearities $f$, and under the Dirichlet exterior condition $u=g$ in $\mathbb{R}^n \setminus Ω$ with general $g$. We establish a uniqueness and a classification result, and we show that weak (energy) stable solutions can be approximated by a sequence of bounded (and hence regular) stable solutions to similar problems. As an application of our results, we establish the interior regularity of weak (energy) stable solutions to the problem for the half-Laplacian in dimensions $1 \leq n \leq 4$.
