This series publishes advanced monographs giving well-written presentations of the "state-of-the-art" in fields of mathematical research that have acquired the maturity needed for such a treatment. They are sufficiently self-contained to be accessible to more than just the intimate specialists of the subject, and sufficiently comprehensive to remain valuable references for many years. Besides the current state of knowledge in its field, an SMM volume should ideally describe its relevance to and interaction with neighbouring fields of mathematics, and give pointers to future directions of research.

No abstract

We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a ∆ 2 nor ∇ 2 -condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to . We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞ -truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces. MSC:46E30, 35J60

No abstract