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

Irregular double-phase evolution problem: Existence and Global regularity
Rakesh Arora
Indian Institute of Technology, Varanasi
India
Co-Author(s):    Sergey Shmarev
Abstract:
This talk presents the existence and regularity results of the homogeneous Dirichlet problem involving the double-phase operator with variable exponents, non-differentiable modulating coefficients and the free term $f$. We establish the existence of a strong solution, which preserves initial temporal integrability, gains global higher integrability and improves second-order regularity.