Entropy solutions of the Dirichlet problem for a class of non-linear elliptic fourth-order equations with right-hand sides in L~1

摘要

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 L~1 for each fixed value of this variable. We prove the existence and uniqueness of an entropy solution. We establish the existence of so-called H-solutions and W-solutions of the problem and prove that the entropy solutions belong to certain Sobolev spaces.