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In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes.
In this paper, we study a semilinear system involving the curl operator in a bounded and convex domain in $R^3$, which comes from the steady-state approximation for Bean critical-state model for type-II superconductors. We show the existence and the
This article concerns with the global Holder regularity of weak solutions to a class of problems involving the fractional $(p,q)$-Laplacian, denoted by $(-Delta)^{s_1}_{p}+(-Delta)^{s_2}_{q}$, for $1<p,q<infty$ and $s_1,s_2in (0,1)$. We use a suitabl
In this paper, we obtain some regularities of the free boundary in optimal transportation with the quadratic cost. Our first result is about the $C^{1,alpha}$ regularity of the free boundary for optimal partial transport between convex domains for de
We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called $varepsilon$-scale fla