On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations

摘要

We present some results on the summability of entropy solutions for the Dirichlet problem in a class of fourth-order non-linear elliptic equations in relation to integrability properties of their right-hand sides. Consideration is given to the cases in which the right-hand sides belong to Lebesgue spaces with exponents close to unity and also to some wider sets contained in L~1.