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arXiv · 2003.05695

Entropy solutions of doubly nonlinear fractional Laplace equations

N. Grossekemper·P. Wittbold·A. Zimmermann
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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.

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N. Grossekemper, P. Wittbold, A. Zimmermann. 2020-03-12. Entropy solutions of doubly nonlinear fractional Laplace equations. https://arxiv.org/abs/2003.05695

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