Analysis of Partial Differential Equations (APDE)
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Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
(20230501)In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces. 
Weighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
(20230315)We prove the sharp mixed Ap−A∞ weighted estimate for the HardyLittlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free ... 
Extrapolation in general quasiBanach function spaces
(20231115)In this work we prove offdiagonal, limited range, multilinear, vectorvalued, and twoweight versions of the Rubio de Francia extrapolation theorem in general quasiBanach function spaces. We prove mapping properties of ... 
ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
(2022)We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596647” regarding the pointwise convergence of ... 
Effective surface energies in nematic liquid crystals as homogenised rugosity effects
(2021)We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques ... 
On C0 and C1 continuity of envelopes of rotational solids and its application to 5axis CNC machining
(202310)We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, ... 
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
(20230101)We establish an asymptotic formula for the number of lattice points in the sets Sh1,h2,h3(λ):={x∈Z+3:⌊h1(x1)⌋+⌊h2(x2)⌋+⌊h3(x3)⌋=λ} with λ∈Z+; where functions h1, h2, h3 are constant multiples of regularly varying functions ... 
On the advectiondiffusion equation with rough coefficients: Weak solutions and vanishing viscosity
(20221101)We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergencefree vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme ... 
Asymptotic behavior of the interface for entire vector minimizers in phase transitions
(20220915)We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of AllenCahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim ua_i^\alpha$ near $u=a_i$, $0<\alpha<2$. ... 
Uniform profile near the point defect of Landaude Gennes model
(20221104)For the Landaude Gennes functional on 3D domains, $$ I_\varepsilon(Q,\Omega):=\int_{\Omega}\left\{\frac12\nabla Q^2+\frac{1}{\varepsilon^2}\left( \frac{a^2}{2}\mathrm{tr}(Q^2)\frac{b^2}{3}\mathrm{tr}(Q^3)+\frac{c^ ... 
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
(20221019)In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential ... 
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
(20231006)In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blowup study ... 
Selfimproving PoincaréSobolev type functionals in product spaces
(2021)In this paper we give a geometric condition which ensures that (q, p)Poincar´eSobolev inequalities are implied from generalized (1, 1)Poincar´e inequalities related to L 1 norms in the context of product spaces. ... 
Eigenvalue Curves for Generalized MIT Bag Models
(2021)We study spectral properties of Dirac operators on bounded domains Ω ⊂ R 3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ ∈ R; the case τ = 0 corresponds to the MIT ... 
Cones with convoluted geometry that always scatter or radiate
(2021)We investigate fixed energy scattering from conical potentials having an irregular crosssection. The incident wave can be an arbitrary nontrivial Herglotz wave. We show that a large number of such local conical scatterers ... 
On the existence of weak solutions for the 2D incompressible Euler equations with inout flow and source and sink points
(2021)Wellposedness for the two dimensional Euler system with given initial vorticity is known since the works of Judoviˇc. In this paper we show existence of solutions in the case where we allowed the fluid to enter in and ... 
The Hajłasz capacity density condition is selfimproving
(2021)We prove a selfimprovement property of a capacity density condition for a nonlocal Haj lasz gradient in complete geodesic spaces. The proof relates the capacity density condition with boundary Poincar´e inequalities, ... 
On quantitative Runge approximation for the time harmonic Maxwell equations.
(2021)Here we derive some results on so called quantitative Runge approximation in the case of the timeharmonic Maxwell equations. This provides a Runge approximation having more explicit quantitative information. We additionally ... 
Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
(2021)We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1D Schr¨odinger map ... 
On the one dimensional cubic NLS in a critical space
(2021)In this note we study the initial value problem in a critical space for the one dimensional Schr¨odinger equation with a cubic nonlinearity and under some smallness conditions. In particular the initial data is given by ...