29 citations · 167 across the 19 of their papers we have counts for
19 papers
Orlicz Potential Theory: Balayage, Riesz Measures, and Very Weak Solutions
Iwona Chlebicka, Minhyun Kim, Ying Li +1
We develop a nonlinear potential theory for elliptic equations with Orlicz growth under general monotonicity and growth conditions, without any homogeneity or scaling assumptions.…
Gradient Riesz potential estimates for a general class of measure data quasilinear systems
Iwona Chlebicka, Minhyun Kim, Marvin Weidner
We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates f…
Curvature bound for Minkowski problem
Kyeongsu Choi, Minhyun Kim, Taehun Lee
We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure with a positive smooth density , any solution to the $L_p…
Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents
Minhyun Kim
A Bourgain--Brezis--Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiti…
The fractional -Laplacian on hyperbolic spaces
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We present three equivalent definitions of the fractional -Laplacian , , , with normalizing constants, on hyperbolic spaces. The expli…
Diameter estimate for planar dual Minkowski problem
Minhyun Kim, Taehun Lee
In this paper, given a prescribed measure on whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar dual M…
The Wiener criterion for nonlocal Dirichlet problems
Minhyun Kim, Ki-Ahm Lee, Se-Chan Lee
We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability and summability . We es…
Harnack inequality for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness a…
Regularity for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of -type and for weak solutions to a related class of nonlocal equ…
The discrete logarithmic Minkowski problem for the electrostatic -capacity
Minhyun Kim, Taehun Lee
The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem ha…
Robust near-diagonal Green function estimates
Moritz Kassmann, Minhyun Kim, Ki-Ahm Lee
We prove sharp near-diagonal pointwise bounds for the Green function for nonlocal operators of fractional order . The novelty of our results is two-fold: the…
Harnack inequality for fractional Laplacian-type operators on hyperbolic spaces
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We establish the Krylov--Safonov theory for a large class of nonlocal operators of order on hyperbolic spaces with curvature . We prove the…
Local regularity for nonlocal equations with variable exponents
Jamil Chaker, Minhyun Kim
In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler--Lagrang…
The concentration-compactness principle for the nonlocal anisotropic -Laplacian of mixed order
Jamil Chaker, Minhyun Kim, Marvin Weidner
In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrabil…
Regularity estimates for fractional orthotropic -Laplacians of mixed order
Jamil Chaker, Minhyun Kim
We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequalit…
Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We establish the Krylov Safonov Harnack inequalities and Holder estimates for fully nonlinear nonlocal operators of non-divergence form on Riemannian manifolds with nonnegative sec…
Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders
Minhyun Kim, Ki-Ahm Lee
We establish the generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to the fra…
Regularity for fully nonlinear integro-differential operators with kernels of variable orders
Minhyun Kim, Ki-Ahm Lee
We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian…
Boundary regularity for nonlocal operators with kernels of variable orders
Minhyun Kim, Panki Kim, Jaehun Lee +1
We study the boundary regularity of solutions of the Dirichlet problem for the nonlocal operator with a kernel of variable orders. Since the order of differentiability of the kerne…