### authors

- LEONORI, TOMMASO
- PERAL, IRENEO
- PRIMO, ANA
- SORIA, FERNANDO

- December 2015

- 6031

- 6068

- 12- NĂºmero especial

- 35

- 1078-0947

- 1553-5231

- In this work we consider the problems { Lu = f in Omega u = 0 in R-N\Omega, and {u(t) + Lu = f in Q(T) Omega x (0, T), u(x, t) = 0 in (R-N\Omega) x (0, T), u(x, 0) = 0 in Omega, where L is a nonlocal differential operator and Omega is a bounded domain in R-N, with Lipschitz boundary. The main goal of this work is to study existence, uniqueness and summability of the solution u with respect to the summability of the datum f. In the process we establish an L-p-theory, for p >= 1, associated to these problems and we prove some useful inequalities for the applications.

- nonlocal operators; elliptic equations; parabolic equations; summability of the solutions