Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces

Iwona Chlebicka is an assistant professor at the University of Warsaw. Her interests focus on nonlinear PDEs with Orlicz and Musielak–Orlicz growth, including their anisotropic variants, and the functional analysis of the underlying function spaces. Investigating elliptic and parabolic problems with data below duality she studies well-posedness of various notions of very weak solutions, as well as their regularity. Piotr Gwiazda is a professor at the Institute of Mathematics of the Polish Academy of Sciences. His wide spectrum of research includes the topics of weak, renormalized and measure-valued solutions to nonlinear PDEs. A substantial part of his contributions concerns elliptic and parabolic equations in Musielak–Orlicz spaces. He is also interested in PDEs arising from fluid and solid mechanics as well as mathematical biology. Agnieszka Świerczewska-Gwiazda is a professor at the University of Warsaw. Her diverse scientific interests include nonlinear PDEs in Musielak–Orlicz spaces as well as hyperbolic conservation laws, entropy methods in fluid dynamics and mathematical biology, weak convergence methods and measure-valued solutions. Aneta Wróblewska-Kamińska is an assistant professor at the Institute of Mathematics of the Polish Academy of Sciences. Her scientific interests include nonlinear PDEs, existence of weak solutions, and their qualitative properties, mathematical models of fluid mechanics, non-Newtonian fluids, Musielak–Orlicz spaces, singular limits, and Navier–Stokes and Euler type equations.    

Part I Overture: 1. Introduction.- 2. N-Functions.- 3. Musielak-Orlicz Spaces.- Part II PDEs: 4. Weak Solutions.- 5. Renormalized Solutions.- 6. Homogenization of Elliptic Boundary Value Problems.- 7. Non-Newtonian Fluids.- Part III Auxiliaries: 8. Basics.- 9. Functional Inequalities.- References.- List of Symbols.- Index.