4 papers
Gradient estimates for parabolic nonlinear nonlocal equations
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
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 o…
Higher differentiability for the fractional -Laplacian
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
In this work, we study the higher differentiability of solutions to the inhomogeneous fractional -Laplace equation under different regularity assumptions on the data. In the sup…
Zaremba problem with degenerate weights
Anna Kh. Balci, Ho-Sik Lee
We establish Zaremba problem for Laplacian and -Laplacian with degenerate weights when the Dirichlet condition is only imposed in a set of positive weighted capacity. We prove w…
Regularity results for mixed local and nonlocal double phase functionals
Sun-Sig Byun, Ho-Sik Lee, Kyeong Song
We investigate the De Giorgi-Nash-Moser theory for minimizers of mixed local and nonlocal functionals modeled after \[ v \mapsto \int_{\mathbb{R}^{n}}\int_{\mathbb{R}^{n}}\dfrac{|v…