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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…