Nonlinear nonlocal potential theory at the gradient level

L Diening, K Kim, HS Lee, S Nowak - arXiv preprint arXiv:2402.04809, 2024 - arxiv.org
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear
nonlocal setting. First of all, we prove that weak solutions to a class of homogeneous …

Gradient estimates for parabolic nonlinear nonlocal equations

L Diening, K Kim, HS Lee, S Nowak - arXiv preprint arXiv:2409.18059, 2024 - arxiv.org
The primary objective of this work is to establish pointwise gradient estimates for solutions to
a class of parabolic nonlinear nonlocal measure data problems, expressed in terms of …

Pointwise and Oscillation Estimates via Riesz Potentials for Mixed Local and Nonlocal Parabolic Equations

L Ma, Q Xiong, Z Zhang - arXiv preprint arXiv:2407.07600, 2024 - arxiv.org
We establish a class of pointwise estimates for weak solutions to mixed local and nonlocal
parabolic equations involving measure data and merely measurable coefficients via caloric …

H\"{o} lder Continuity for Fully Fractional Parabolic Equations with Space-time Nonlocal Operators

L Ma, Q Xiong, Z Zhang - arXiv preprint arXiv:2406.08795, 2024 - arxiv.org
We study the local H\"{o} lder regularity of weak solutions to the fully fractional parabolic
equations involving spatial fractional diffusion and fractional time derivatives of the …