7 papers · 1 filter
Self-improving properties for the fractional -Laplacian via nonlinear commutators
Ho-Sik Lee, Kyeong Song
We investigate a class of nonlocal equations whose leading operator is modeled on either the fractional -Laplacian or the regional fractional -Laplacian, .…
Gradient estimates for singular elliptic measure data problems with double phase
Kyeong Song, Yeonghun Youn, Anna Zatorska-Goldstein
We consider elliptic measure data problems of the type \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = μ\] in a bounded domain in , where and $a(\cdot) \ge…
Gradient estimates for degenerate elliptic measure data problems with double phase
Kyeong Song, Yeonghun Youn
We study nonlinear elliptic equations modeled on \[ -\mathrm{div}\,(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du) = μ, \] where , , and is a signed Borel meas…
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…
Riesz potential estimates for mixed local-nonlocal problems with measure data
Iwona Chlebicka, Kyeong Song, Yeonghun Youn +1
We study gradient regularity for mixed local-nonlocal problems modelled upon \[ -Δ_p u +(-Δ_p)^su=μ\qquad\text{for} \quad 2-\tfrac{1}{n}<p<\infty\quad \text{and}\quad s\in(0,1)\,,\…
Singular elliptic measure data problems with irregular obstacles
Sun-Sig Byun, Kyeong Song, Yeonghun Youn
We investigate elliptic irregular obstacle problems with -growth involving measure data. Emphasis is on the strongly singular case , and we obtain several new c…