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4 papers · 2 filters
Existence of mixed type solutions in the Chern-Simons gauge theory of rank two in
Kwangseok Choe, Namkwon Kim, Youngae Lee +1
We consider the Chern-Simons gauge theory of rank such as , , and Chern-Simons model in . There may exist three types of solutions in these th…
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) $…
Nondivergence elliptic and parabolic problems with irregular obstacles
Sun-Sig Byun, Ki-Ahm Lee, Jehan Oh +1
We prove the natural weighted Calderón and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irr…
The Regularity Theory for the Double Obstacle Problem
Ki-ahm Lee, Jinwan Park, Henrik Shahgholian
In this paper, we prove local regularity of free boundaries for the double obstacle problem with an upper obstacle , \begin{align*} Δu &=fχ_{Ω(u) \cap\{ u< ψ\} }+ Δψχ_{Ω…