Fractional decay bounds for nonlocal zero order heat equations
نویسندگان
چکیده
In this paper we obtain bounds for the decay rate for solutions to the nonlocal problem ∂tu(t, x) = R n J(x, y)[u(t, y) − u(t, x)]dy. Here we deal with bounded kernels J but with polynomial tails, that is, we assume a lower bound of the form J(x, y) ≥ c1|x − y| −(n+2σ) , for |x − y| > c2. Our estimates takes the form u(t) L q (R n) ≤ Ct − n 2σ (1− 1 q) for t large.
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