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On the differentiability of very weak solutions with right-hand side data integrable with respect to the distance to the boundary


Díaz Díaz, Jesús Ildefonso and Rakotoson, Jean Michel Theresien (2009) On the differentiability of very weak solutions with right-hand side data integrable with respect to the distance to the boundary. Journal of Functional Analysis , 257 (3). pp. 807-831. ISSN 0022-1236

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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.

Item Type:Article
Uncontrolled Keywords:Very weak solutions; Distance to the boundary; Regularity; Linear PDE; Monotone rearrangement; Lorentz space
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15112

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