6 papers
Hölder regularity for the parabolic perturbed fractional 1-Laplace equations
Dingding Li, Chao Zhang
This paper studies the regularity of weak solutions to a class of parabolic perturbed fractional -Laplace equations. Our analysis combines finite difference quotients, energy es…
Sobolev regularity for the perturbed fractional 1-Laplace equations in the subquadratic case
Dingding Li, Chao Zhang
This work investigates the Sobolev regularity of solutions to perturbed fractional 1-Laplace equations. Under the assumption that weak solutions are locally bounded, we establish t…
Sobolev regularity for the nonlocal -Laplace equations in the superquadratic case
Dingding Li, Chao Zhang
We investigate the interior Sobolev regularity of weak solutions to the nonlocal -Laplace equations in the superquadratic case . As a product, the explicit Hölder c…
Higher Sobolev regularity for mixed local and nonlocal equations with nonstandard growth
Yuzhou Fang, Dingding Li, Chao Zhang
We develop a systematic study of the interior Sobolev regularity of weak solutions to the mixed local and nonlocal -Laplace equations, which model the superposition of two s…
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…
On the solutions of nonlocal 1-Laplacian equation with -data
Dingding Li, Chao Zhang
We study the solutions to a nonlocal 1-Laplacian equation given by $$ 2\text{P.V.}\int_{\mathbb{R}^N}\frac{u(x)-u(y)}{|u(x)-u(y)|} \frac{dy}{|x-y|^{N+s}}=f(x) \quad \textmd{for } x…