论文标题
内部Hölder规律性，用于稳定解决方案的半线性椭圆方程，直至尺寸5
Interior Hölder regularity for stable solutions to semilinear elliptic equations up to dimension 5
论文作者
论文摘要
令$ 2 \ le n \ le 5 $。我们在任何非线性$ f \ in C^{0,1}（r）$中的任何域中，在任何$ r^n $的任何域中，在任何$ r^n $的任何域中，我们建立了$ c^2 $稳定的解决方案$ c^2 $稳定的解决方案。 $ w^{1,2}（ω）$ - 稳定的解决方案通过$ c^2（ω）$ - 稳定解决方案局部近似它们。特别是，我们不需要$ f $上的任何下限。
Let $2\le n\le 5$. We establish an apriori interior Hölder regularity of $C^2$-stable solutions to the semilinear equation $-Δu=f(u)$ in any domain of $R^n$ for any nonlinearity $f\in C^{0,1}(R) $.If $f $ is nondecreasing and convex in addition,we obtain an interior Hölder regularity, and hence the local boundedness, of $W^{1,2}(Ω)$-stable solutions by locally approximating them via $C^2(Ω)$-stable solutions. In particular, we do not require any lower bound on $f$.
