Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs

DOUBLE PHASE PROBLEMS WITH EXPONENTS DEPENDING ON SOLUTIONS AND THEIR GRADIENTS
Anouar Bahrouni
University of Monastir
Tunisia
Co-Author(s):    Ala Eddine Bahrouni and Hlel Missaoui
Abstract:
In this talk,, we introduce two novel classes of quasilinear elliptic equations, each driven by the double phase operator with variable exponents. The first class features a new double phase equation where exponents depend on the gradient of the solution. In the second category, the treatment of exponents is dependent on the solution itself. This class differs from the first one due to the unavailability of suitable Musielak-Orlicz Sobolev spaces. For this reason, we employ a perturbation argument that leads to the classical double phase class.