Contributions to Books:
A. Menovschikov, A. Molchanova, L. Scarpa:
"An extended variational theory for nonlinear evolution equations via modular spaces";
in: "ASC Report 39/2020",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reﬂexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based on abstract modular spaces associated to a given convex function. Firstly, we show that the new variational triple is suited for framing the evolu-tion, in the sense that a novel duality paring can be introduced and a generalised computational chain rule holds. Secondly, we prove well-posedness in an extended variational sense for evolu-tion equations, without relying on any reﬂexivity assumption and any polynomial requirement on the nonlinearity. Finally, we discuss several important applications that can be addressed in this framework: these cover, but are not limited to, equations in Musielak-Orlicz-Sobolev spaces, such as variable exponent, Orlicz, weighted Lebesgue, and double-phase spaces.
Nonlinear evolution equations; variational approach; modular spaces; Musielak-Orlicz-Sobolev spaces.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.