Abstract
AbstractIn this contribution, we study a class of doubly nonlinear elliptic equations with bounded, merely integrable right-hand side on the whole space $$\mathbb {R}^N$$
R
N
. The equation is driven by the fractional Laplacian $$(-\varDelta )^{\frac{s}{2}}$$
(
-
Δ
)
s
2
for $$s\in (0,1]$$
s
∈
(
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 $$L^1$$
L
1
-contraction and comparison principle and to show existence and uniqueness of entropy solutions.
Funder
Universität Duisburg-Essen
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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