Entropy solutions of the Dirichlet problem for a class of non-linear elliptic fourth-order equations with right-hand sides in $ L^1$
Александр Альбертович Ковалевский · Izvestiya Mathematics · 2001
In this paper we introduce and study the notion of an entropy solution of the Dirichlet problem for a class of non-linear elliptic fourth-order equations whose right-hand sides admit arbitrary growth with respect to the variable corresponding to the unknown function and belong to the space for each fixed value of this variable. We prove the existence and uniqueness of an entropy solution. We establish the existence of so-called -solutions and -solutions of the problem and prove that the entropy solutions belong to certain Sobolev spaces.