5 papers
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…
estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form
Sun-Sig Byun, Kyeongbae Kim
We study -fractional -Laplacian type equations with discontinuous kernel coefficients in divergence form to establish estimates for any choice of pairs w…
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…
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…
Local Hölder continuity for fractional nonlocal equations with general growth
Sun-Sig Byun, Hyojin Kim, Jihoon Ok
We study generalized fractional -Laplacian equations to prove local boundedness and Hölder continuity of weak solutions to such nonlocal problems by finding a suitable fractiona…