11 citations · 20 across the 6 of their papers we have counts for
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A geometric result for composite materials with -boundaries
Youchan Kim, Pilsoo Shin
In this paper, we obtain a geometric result for composite materials related to elliptic and parabolic partial differential equations. In the classical papers Li and Vogelius (2000)…
Gradient type estimates for linear elliptic systems from composite materials
Youchan Kim, Pilsoo Shin
In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We d…
Regularity estimates for singular parabolic measure data problems with sharp growth
Jung-Tae Park, Pilsoo Shin
We prove global gradient estimates for parabolic -Laplace type equations with measure data, whose model is $$u_t - \textrm{div} \left(|Du|^{p-2} Du\right) = μ\quad \textrm{in} \…
Global regularity for degenerate/singular parabolic equations involving measure data
Sun-Sig Byun, Jung-Tae Park, Pilsoo Shin
We consider degenerate and singular parabolic equations with -Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite tot…
Global Sobolev regularity for general elliptic equations of -Laplacian type
Sun-Sig Byun, Dian K. Palagachev, Pilsoo Shin
We derive global gradient estimates for -weak solutions to quasilinear elliptic equations of the form $$ \mathrm{div\,}\mathbf{a}(x,u,Du)=\mathrm{div\,}(|F|^{p-2}F) $…
Global Hoelder continuity of solutions to quasilinear equations with Morrey data
Sun-Sig Byun, Dian K. Palagachev, Pilsoo Shin
We deal with general quasilinear divergence-form coercive operators whose prototype is the -Laplacean operator. The nonlinear terms are given by Carathéodory functions and satis…