论文标题
双线非线性拉普拉斯方程的熵溶液
Entropy solutions of doubly nonlinear fractional Laplace equations
论文作者
论文摘要
在这一贡献中，我们研究了一类双重非线性椭圆方程，在整个空间上，有界，仅在整个空间上进行右侧$ \ mathbb {r}^n $。该方程是由分数拉普拉斯$（ - δ）^{\ frac {s} {2}} $ for $ s \ in（0,1] $驱动的，并且在（0,1] $中$ s \ in（0,1] $，一个强烈的非线性对第一阶的非线性扰动。在这种情况下，$ l^1 $ l^1 $ l^1 $ l^1 $ l^1 $ l^1 $。熵解决方案的独特性。
In this contribution, we study a class of doubly nonlinear elliptic equations with bounded, merely integrable right-hand side on the whole space $\mathbb{R}^N$. The equation is driven by the fractional Laplacian $(-Δ)^{\frac{s}{2}}$ for $s\in (0,1]$ and a strongly continuous nonlinear perturbation of first order. It is well known that weak solutions are in genreral not unique in this setting. We are able to prove an $L^1$-contraction and comparison principle and to show existence and uniqueness of entropy solutions.
