Abstract
In this paper, we obtain bounds for the decay rate for solutions to the nonlocal problem ∂ t u ( t , x ) = ∫ R n J ( x , y ) [ u ( t , y ) − u ( t , x ) ] d y . Here we deal with bounded kernels J but with polynomial tails, that is, we assume a lower bound of the form J ( x , y ) ⩾ c 1 | x − y | − ( n + 2 σ ) , for | x − y | > c 2 . Our estimates takes the form ∥ u ( t ) ∥ L q ( R n ) ⩽ C t − ( n / 2 σ ) ( 1 − 1 / q ) for t large.
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