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Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation
(2016-12-31)
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ...
A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions
Ourmières-Bonafos, T.; Vega, L.
(2016-12-21)
(2016-12-21)
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...
Dimension reduction for the micromagnetic energy functional on curved thin films
(2016-12-14)
Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context
of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared.
In particular, thin ...
On the controllability of Partial Differential Equations involving non-local terms and singular potentials
(2016-12-12)
In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ...
New bounds for bilinear Calderón-Zygmund operators and applications
(2016-11-25)
In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ...
Reconstruction from boundary measurements for less regular conductivities
(2016-10-01)
In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$
or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz ...
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(2016-09-10)
We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ...
Hardy uncertainty principle, convexity and parabolic evolutions
Escauriaza, L.; Kenig, C.E.; Ponce, G.; Vega, L. (2016-09-01)
(2016-09-01)
We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of ...
Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type
(2016-09-01)
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ ...
Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations
(2016-09-01)
The Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting ...