Leonori, TommasoPeral, IreneoPrimo, AnaSoria, Fernando2024-11-212024-11-212015-12Tommaso Leonori, Ireneo Peral, Ana Primo, Fernando Soria. Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations. Discrete and Continuous Dynamical Systems, 2015, 35(12): 6031-6068. doi: https://doi.org/10.3934/dcds.2015.35.60311078-0947; eISSN: 1553-5231https://doi.org/10.3934/dcds.2015.35.6031https://hdl.handle.net/20.500.14468/24457In this work we consider the problems { script Lu = f in Ω, u = 0 in ℝN\Ω, and { ut + script Lu = f in QT ≡ Ω x (0,T), u(x,t) = 0 in (ℝN\Ω) x (0,T), u(x, 0) = 0 in Ω, where script L is a nonlocal differential operator and Ω is a bounded domain in ℝN, 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 Lp-theory, for p ≥ 1, associated to these problems and we prove some useful inequalities for the applications.eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoNonlocal operatorselliptic equationsparabolic equationssummability of the solutions