On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result

Abstract

In this paper we prove the compactness of the embeddings of the space of radially symmetric functions of BL(R N) into some Lebesgue spaces. In order to do so we prove a regularity result for solutions of the Poisson equation with measure data in R N, as well as a version of the Radial Lemma of Strauss to the space BL(R N). An application is presented involving a quasilinear elliptic problem of higher-order, where variational methods are used to find the solutions.