On a singular anisotropic parabolic equation related to the $\vec{p}(x)$-Laplacian
Year: 2026
Type: article
Abstract: This paper investigates a singular anisotropic parabolic equation associated with the pi(x)$p_{i}(x)$-Laplacian operator. By employing the anisotropic Gagliardo-Sobolev-Nirenberg inequality and a modified Di Giorgi iteration technique, we derive a uniform L∞$L^{\infty}$-estimate for the weak solution un$u_{n}$ of the approximate problem. Using the Hölder inequality and embedding theorems in anisotropic Sobolev spaces, we successfully eliminate the effects of both the damping and source terms. Furthermore, using Egoroff’s theorem, we prove the strong convergence of unxi→u$u_{nx_{i}}\rightarrow u$ in the Lpi(x)(QT)$L^{p_{i}(x)}(Q_{T})$ space. The existence of a weak solution is finally confirmed through the renormalized solution method.
Source: Boundary Value Problems
Authors: Qitong Ou, Huashui Zhan
Institution: Xiamen University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,890
OpenAlex ID: W7118585908