5 papers
Nonlinear nonlocal equations in Reifenberg flat domains
Sun-Sig Byun, Kyeongbae Kim, Kyeong Song
We consider nonhomogeneous fractional -Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption o…
Global Calderón-Zygmund theory for fractional Laplacian type equations
Sun-Sig Byun, Kyeong Bae Kim, Deepak Kumar
We establish several fine boundary regularity results of weak solutions to non-homogeneous -fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund t…
Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients
Sun-Sig Byun, Kyeongbae Kim, Deepak Kumar
We prove Calderón-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particu…
Higher Hölder regularity for nonlocal parabolic equations with irregular kernels
Sun-Sig Byun, Hyojin Kim, Kyeongbae Kim
We study a nonlocal parabolic equation with an irregular kernel coefficient to establish higher Hölder regularity under an appropriate higher integrablilty on the nonhomogeneous te…
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…