Díaz Díaz, Jesús IldefonsoRakotoson, Jean Michel Theresien2023-06-202023-06-202009-08-010022-123610.1016/j.jfa.2009.03.002https://hdl.handle.net/20.500.14352/42162We 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022123609001177http://www.sciencedirect.com/restricted access517.98Very weak solutionsDistance to the boundaryRegularityLinear PDEMonotone rearrangementLorentz spaceAnálisis funcional y teoría de operadores