Ho-Sik Lee

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math.AP2024

Higher differentiability for the fractional $p$ -Laplacian

Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1

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 sup…

math.AP2024

Zaremba problem with degenerate weights

Anna Kh. Balci, Ho-Sik Lee

We establish Zaremba problem for Laplacian and $p$ -Laplacian with degenerate weights when the Dirichlet condition is only imposed in a set of positive weighted capacity. We prove w…

math.AP2023

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…

Higher differentiability for the fractional p-Laplacian

Zaremba problem with degenerate weights

Regularity results for mixed local and nonlocal double phase functionals

Higher differentiability for the fractional $p$ -Laplacian