The long-time behavior of weighted p-Laplacian equations - Ma, Shan; Li, Hongtao (Topological Methods in Nonlinear Analysis, 2019)
In this work we study weighted p-Laplacian equations in abounded domain with a variable and generally non-smooth diffusion coefficient having at most a finite number of zeroes. The main attention is focused on the case that the diffusion coefficient a(x) in such equations satisfies the inequality _x→ z|x-z|^-pa(x)> 0 for every zΩ. We show the existence of weak solutions and global attractors in L^2(Ω), L^q(Ω)(q≥ 2) and D_0^1,p(Ω), respectively.