Quasilincar elliptic problems with general growth and merely integrable, or measure, data

Boundary value problems for a class of quasilinear elliptic equations, with an Orlicz type growth and L-1 right-hand side are considered. Both Dirichlet and Neumann problems are contemplated. Existence and uniqueness of generalized solutions, as well as their regularity, are established. The case of measure right-hand sides is also analyzed. (C) 2017 Published by Elsevier Ltd.
Funding Agencies|Research Project of the Italian Ministry of University and Research (MIUR) Prin [2015HY8JCC]; GNAMPA of the Italian INdAM (National Institute of High Mathematics); Ministry of Education and Science of the Russian Federation [02.a03.21.0008]