Kyeongbae Kim

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math.AP2025

Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem

Kyeongbae Kim, Ho-Sik Lee, Harsh Prasad

We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in…

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.AP2023

$L^{q}$ estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form

Sun-Sig Byun, Kyeongbae Kim

We study $s$ -fractional $p$ -Laplacian type equations with discontinuous kernel coefficients in divergence form to establish $W^{s + σ, q}$ estimates for any choice of pairs $(σ, q)$ w…

math.AP2023

Regularity results for a class of nonlocal double phase equations with VMO coefficients

Sun-Sig Byun, Kyeongbae Kim, Deepak Kumar

We study a class of nonlocal double phase problems with discontinuous coefficients. A local self-improving property and a higher Hölder continuity result for weak solutions to such…

Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem

Higher differentiability for the fractional p-Laplacian

Lq estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form

Regularity results for a class of nonlocal double phase equations with VMO coefficients

Higher differentiability for the fractional $p$ -Laplacian

$L^{q}$ estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form