On a fractional sublinear elliptic equation with a variable coefficient

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.

Keywords:

• fractional Laplacian
• sublinear elliptic equations
• Riesz potential
• well-posedness
• porous medium equation

AMS Subject Classifications:

• 35A01
• 35A02
• 35J61
• 35K65
• 35R11

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].