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00925njm 22002777a 4500 dc Díaz Díaz, Jesús Ildefonso author Rakotoson, Jean Michel Theresien author 2009-08-01 We study the differentiability of very weak solutions v is an element of L(1) (Omega) of (v, L* phi)(0) = (f, phi)(0) for all phi is an element of C(2)((Omega) over bar) vanishing at the boundary whenever f is in L(1) (Omega, delta), with delta = dist(x, partial derivative Omega), and L* is a linear second order elliptic operator with variable coefficients. We show that our results are optimal. We use symmetrization techniques to derive the regularity in Lorentz spaces or to consider the radial solution associated to the increasing radial rearrangement function (f) over tilde of f. 0022-1236 10.1016/j.jfa.2009.03.002 https://hdl.handle.net/20.500.14352/42162 http://www.sciencedirect.com/science/article/pii/S0022123609001177 http://www.sciencedirect.com/ On the differentiability of very weak solutions with right-hand side data integrable with respect to the distance to the boundary