We establish small energy H\"{o}lder bounds for minimizers $u_\varepsilon$ of \[E_\varepsilon (u):=\int_\Omega W(\nabla u)+ \frac{1}{\varepsilon^2} \int_\Omega f(u),\] where $W$ is a positive definite quadratic form and the potential $f$ constrains $u$ to be close to a given manifold $\mathcal N$. This implies that, up to subsequence, $u_\varepsilon$ converges locally uniformly to an $\mathcal N$-valued $W$-harmonic map, away from its singular set. We treat general energies, covering in particular the 3D Landau-de Gennes model for liquid crystals, with three distinct elastic constants. Similar results are known in the isotropic case $W(\nabla u)=\vert \nabla u\vert^2$ and rely on three ingredients: a monotonicity formula for the scale-invar...
For the Landau-de Gennes functional on 3D domains, $$ I_\varepsilon(Q,\Omega):=\int_{\Omega}\left\...
In this paper we prove that the singular set of connected minimizers of the planar Griffith function...
We show local higher integrability of derivative of a suitable weak solution to the surface growth m...
We study minimizers of a family of functionals $E_\varepsilon$ indexed by a characteristic length sc...
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory o...
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge...
AbstractIn this paper we discuss the convergence behavior of a sequence of α-harmonic maps uα with E...
We study the asymptotic behaviour, as a small parameter ε tends to zero, of minimisers of a Ginzburg...
Let (M,g) be a smooth, compact Riemannian manifold with smooth boundary, with n = dim M = 2, 3. We s...
In the first part of the thesis we consider elliptic systems in the critical dimension $2m$ that con...
We study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is ...
AbstractWe prove that every minimizer on H1(Ω; S2) of the relaxed energy ∝¦▽u¦2 + 8πλL(u), where 0 ⩽...
AbstractWe characterize weak limits of sequences of smooth functions from Bn into suitable manifolds...
We describe a new approach to understanding averages of high energy Laplace eigenfunctions, uh, over...
We prove the energy identity for the Sacks-Uhlenbeck and the biharmonic approximation of harmonic ma...
For the Landau-de Gennes functional on 3D domains, $$ I_\varepsilon(Q,\Omega):=\int_{\Omega}\left\...
In this paper we prove that the singular set of connected minimizers of the planar Griffith function...
We show local higher integrability of derivative of a suitable weak solution to the surface growth m...
We study minimizers of a family of functionals $E_\varepsilon$ indexed by a characteristic length sc...
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory o...
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge...
AbstractIn this paper we discuss the convergence behavior of a sequence of α-harmonic maps uα with E...
We study the asymptotic behaviour, as a small parameter ε tends to zero, of minimisers of a Ginzburg...
Let (M,g) be a smooth, compact Riemannian manifold with smooth boundary, with n = dim M = 2, 3. We s...
In the first part of the thesis we consider elliptic systems in the critical dimension $2m$ that con...
We study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is ...
AbstractWe prove that every minimizer on H1(Ω; S2) of the relaxed energy ∝¦▽u¦2 + 8πλL(u), where 0 ⩽...
AbstractWe characterize weak limits of sequences of smooth functions from Bn into suitable manifolds...
We describe a new approach to understanding averages of high energy Laplace eigenfunctions, uh, over...
We prove the energy identity for the Sacks-Uhlenbeck and the biharmonic approximation of harmonic ma...
For the Landau-de Gennes functional on 3D domains, $$ I_\varepsilon(Q,\Omega):=\int_{\Omega}\left\...
In this paper we prove that the singular set of connected minimizers of the planar Griffith function...
We show local higher integrability of derivative of a suitable weak solution to the surface growth m...