相关论文: Regularity of capillarity droplets with obstacle
In this paper we study existence and regularity of solutions to the capillarity problem for compressible liquids in a tube. We introduce an appropriate space of functions of bounded variation, in which the energy functional recently…
In this paper, we establish an $\varepsilon$-regularity theorem for minimizers of an Alt-Phillips type functional subject to constraint maps. We prove that under sufficiently small energy, the minimizers exhibit regularity, and hence…
We investigate minimizers defined on a bounded domain $\Omega$ in $\mathbb{R}^2$ for singular constrained energy functionals that include Ball and Majumdar's modification of the Landau-de Gennes Q-tensor model for nematic liquid crystals.…
We investigate minimizers defined on a bounded domain in $\mathbb{R}^2$ for the Maier--Saupe Q--tensor energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Mujamdar's modification…
We investigate properties of minimizers of a variational model describing the shape of charged liquid droplets. The model, proposed by Muratov and Novaga, takes into account the regularizing effect due to the screening of free…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
Motived by the heat flow and bubble analysis of biharmonic mappings, we study further regularity issues of the fourth order Lamm-Riviere system $$\Delta^{2}u=\Delta(V\cdot\nabla u)+{\rm div}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f$$ in…
We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small volume minimizers are convex and uniformly close to a ball.
We provide a quantitative description of global minimizers of the Gauss free energy for a liquid droplet bounded in a container in the small volume regime.
We study the regularity of minimizers for a variant of the soap bubble cluster problem: \begin{align*} \min \sum_{\ell=0}^N c_{\ell} P( S_\ell)\,, \end{align*} where $c_\ell>0$, among partitions $\{S_0,\dots,S_N,G\}$ of $\mathbb{R}^2$…
We study the partial regularity of minimizers for certain singular functionals in the calculus of variations, motivated by Ball and Majumdar's recent modification [BM] of the Landau-de Gennes energy functional.
We establish an $\varepsilon$-regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, as a consequence, the partial regularity of such BV…
We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…
Motivated by the construction of time-periodic solutions for the three-dimensional Landau-Lifshitz-Gilbert equation in the case of soft and small ferromagnetic particles, we investigate the regularity properties of minimizers of the…
We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $\theta \in (0,\pi)$ and dimension $n \geq 2$. As a consequence, we obtain the generalized…
We establish partial regularity for the $\omega$-minimizers of quasiconvex functionals of power growth. A first-order partial regularity result of $BV$ $\omega$-minimizers is obtained in the linear growth case under a Dini-type condition on…
In this note we study the boundary regularity of minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularity in all dimensions $n\geq 3 .$ In dimension $n=3,$ this…
Motivated by Ball and Majumdar's modification of Landau-de Gennes model for nematic liquid crystals, we study energy-minimizer $Q$ of a tensor-valued variational obstacle problem in a bounded 3-D domain with prescribed boundary data. The…
A partial regularity theorem is presented for minimisers of $k$th-order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an $N$-function satisfying the $\Delta_2$…
We give partial boundary regularity for co-dimension one absolutely area-minimizing currents at points where the boundary consists of a sum of $C^{1,\alpha}$ submanifolds, possibly with multiplicity, meeting tangentially, given that the…