Jihoon Ok

Parabolic systems with measurable coefficients in weighted Orlicz spaces

We consider a parabolic system in divergence form with measurable coefficients in a cylindrical space–time domain with nonsmooth base. The associated nonhomogeneous term is assumed to belong to a suitable weighted Orlicz space. Under possibly optimal assumptions on the coefficients and minimal geometric requirements on the boundary of the underlying domain, we generalize the Calderon–Zygmund theorem for such systems by essentially proving that the spatial gradient of the weak solution gains the same weighted Orlicz integrability as the nonhomogeneous term.

Global gradient estimates for nonlinear obstacle problems with nonstandard growth

Abstract We investigate an optimal W 1 , p ⁢ ( ⋅ ) ⁢ q

Nonlinear Parabolic Equations with Variable Exponent Growth in Nonsmooth Domains

{W^{1,p(\,\cdot\,)q}}

Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains

-regularity theory for a nonlinear elliptic obstacle problem with nonstandard growth p ⁢ ( ⋅ )

Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity

{p(\,\cdot\,)}

On W1,q(⋅)-estimates for elliptic equations of p(x)-Laplacian type

. With a sufficient small log-Hölder constant on p ⁢ ( ⋅ )

Gradient estimates for elliptic equations with \(L^{p(\cdot )}\log L\) growth

{p(\,\cdot\,)}

W 1, p(·)-Regularity for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

, under a suitable smallness condition in BMO on the nonlinearity and under a sufficient flatness condition on the boundary of the domain, we establish a global Calderón–Zygmund estimate for such an irregular obstacle problem by proving that the gradient of the weak solution is as integrable as both the gradient of the obstacle and the inhomogeneous term in the variable exponent space L p ⁢ ( ⋅ ) ⁢ q

W^{2,p(\cdot )}-regularity for elliptic equations in nondivergence form with BMO coefficients

{L^{p(\,\cdot\,)q}}

Regularity results for a class of obstacle problems with nonstandard growth

for every q ∈ ( 1 , ∞ )