Abstract
We study the existence and uniqueness of bounded weak solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the proof of uniqueness relies on uniqueness of weak solutions to an associated fractional porous medium equation with variable density.
Acknowledgments
We would like to thank the anonymous Referees for their very interesting comments that allow us to improve some parts of the paper.
Notes
1 Gabriele Terrone was supported by the UTAustin-Portugal partnership through the FCT post-doctoral fellowship SFRH/BPD/40338/2007, CAMGSD-LARSys through FCT Program POCTI – FEDER and by [grant number PTDC/MAT/114397/2009], [grant number UTAustin/MAT/0057/2008], and [grant number UTA-CMU/MAT/0007/2009].