Higher differentiability for the fractional -Laplacian

L Diening, K Kim, HS Lee, S Nowak - arXiv preprint arXiv:2406.16727, 2024 - arxiv.org
In this work, we study the higher differentiability of solutions to the inhomogeneous fractional
$ p $-Laplace equation under different regularity assumptions on the data. In the …

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 …