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math.AP2024
Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation
Dingding Li, Chao Zhang
We consider a class of parabolic nonlocal -Laplacian equation \begin{align*} u_t+(-Δ)^s_1u=f \quad \text{ in }Ω\times(0,T]. \end{align*} By employing the Rothe time-discretizati…
math.AP2024
Generalized Young Measure Solutions for a Class of Quasilinear Parabolic Equations with Linear Growth
Jingfeng Shao, Zhichang Guo, Chao Zhang
Using the generalized Young measure theory, we extend the theory of Young measure solutions to a class of quasilinear parabolic equations with linear growth, and introduce the conc…
math.AP2024
On the weak Harnack inequalities for nonlocal double phase problems
Yuzhou Fang, Chao Zhang
This paper is devoted to studying the weak Harnack inequalities for nonlocal double phase functionals by using expansion of positivity, whose prototype is $$ \iint_{\mathbb{R}^n\ti…