Entropy solutions of doubly nonlinear fractional Laplace equations

Abstract

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 $(-\Delta {)}^{\frac{s}{2}}$ 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.