• Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces 

  Nieraeth, Z.; Rey, G. (2023-05-01)

  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 

  Accomazzo, N.; Duoandikoetxea, J.; Nieraeth, Z.; Ombrosi, S.; Pérez, C. (2023-03-15)

  We prove the sharp mixed Ap−A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free ...

• Extrapolation in general quasi-Banach function spaces 

  Nieraeth, Z. (2023-11-15)

  In this work we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of ...

• ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2 

  Lucà, R. (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), 596-647” regarding the pointwise convergence of ...

• Effective surface energies in nematic liquid crystals as homogenised rugosity effects 

  Ceuca, R.D.; Taylor, J.M.; Zarnescu, A. (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 5-axis CNC machining 

  Ponce Vanegas, F.; Bizzarri, M.; Barton, M. (2023-10)

  We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis 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 

  Iosevich, A.; Langowski, B.; Mirek, M.; Szarek, T.Z. (2023-01-01)

  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 advection-diffusion equation with rough coefficients: Weak solutions and vanishing viscosity 

  Bonicatto, P.; Ciampa, G.; Crippa, G. (2022-11-01)

  We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergence-free 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 

  Alikakos, N.; Geng, Z.; Zarnescu, A. (2022-09-15)

  We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of Allen-Cahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim |u-a_i|^\alpha$ near $u=a_i$, $0<\alpha<2$. ...

• Uniform profile near the point defect of Landau-de Gennes model 

  Geng, Z.; Zarnescu, A. (2022-11-04)

  For the Landau-de 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 

  Geng, Z.; Granero-Belinchón, R. (2022-10-19)

  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 

  Lai, N-A; Schiavone, N.M. (2023-10-06)

  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 blow-up study ...

• Self-improving Poincaré-Sobolev type functionals in product spaces 

  Cejas, M.E.; Mosquera, C.; Pérez, C.; Rela, E. (2021)

  In this paper we give a geometric condition which ensures that (q, p)-Poincar´e-Sobolev 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 

  Arrizabalaga, N.; Mas, A.; Sanz-Perela, T.; Vega, L. (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 

  Blåsten, E.L.K.; Pohjola, V. (2021)

  We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be an arbitrary non-trivial 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 in-out flow and source and sink points 

  Bravin, M. (2021)

  Well-posedness 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 self-improving 

  Canto, J.; Vähäkangas, A.V. (2021)

  We prove a self-improvement 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. 

  Pohola, V. (2021)

  Here we derive some results on so called quantitative Runge approximation in the case of the time-harmonic 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 

  Banica, V.; Vega, L. (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 1-D Schr¨odinger map ...

• On the one dimensional cubic NLS in a critical space 

  Bravin, M.; Vega, L. (2021)

  In this note we study the initial value problem in a critical space for the one dimensional Schr¨odinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by ...

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