|Titolo||Weigthed fractional porous media equations: exixtende and uniqueness of weak solution with measure data|
|Autore/i||Grillo, G.; Muratori, M.; Punzo, F.|
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|Abstract||We shall prove existence and uniqueness of solutions to a class of porous media equations driven by weighted fractional Laplacians when the initial data are positive finite measures on the Euclidean space R^d . In particular, Barenblatt-type solutions exist and are unique for the evolutions considered. The weight can be singular at the origin, and must have a sufficiently slow decay at infinity (power-like). Such kind of evolutions seems to have not been treated before even as concerns their linear, non-fractional analogues.