Analysis of Partial Differential Equations (APDE)

Bilinear Spherical Maximal Functions of Product Type

Roncal, L.

; Shrivastava, S.; Shuin, K. (2021-08-12)

In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ...

Variation bounds for spherical averages

Beltran, D.; Oberlin, R.; Roncal, L.

; Stovall, B.; Seeger, A. (2021-06-22)

We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates

On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Della Porta, F.; Rüland, A.; Taylor, J.M.

; Zillinger, C. (2021-07-01)

Building on the work by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv:1810.04380), Torrents et al (2017 Phys. Rev. E 95 ...

Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol

Eceizabarrena, D.; Ponce Vanegas, F.

(2021-08-24)

We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...

A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores

Smyrnelis, P.A.

(2021)

We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ...

Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics

Deng, Y.; Zillinger, C. (2021-07-30)

In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to ...

Leaky Cell Model of Hard Spheres

Fai, Tomas G.; Virga, Epifanio G.; Zheng, Xiaoyu; Palffy-Muhoray, Peter (9-03-20)

We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without ...

Double layered solutions to the extended Fisher–Kolmogorov P.D.E.

Smyrnelis, P. (2021-06-22)

We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ...

RESTRICTED TESTING FOR POSITIVE OPERATORS

Hytönen, T.; Li, K.; Sawyer, E. (2020)

We prove that for certain positive operators T, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant D>1, depending only on the dimension n, such that the two weight norm inequality ...

Static and Dynamical, Fractional Uncertainty Principles

Kumar, S.; Ponce-Vanegas, F.; Vega, L.

(2021-03)

We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...

Extensions of the John-Nirenberg theorem and applications

Canto, J.; Pérez, C. (2021)

The John–Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the ...

Convergence over fractals for the Schrödinger equation

Luca, R.; Ponce-Vanegas, F. (2021-01)

We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ...

Multilinear operator-valued calderón-zygmund theory

Di Plinio, F.; Li, K.; Martikainen, H.; Vuorinen, E. (2020)

We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness ...

Invariant measures for the dnls equation

Lucà, R.

(2020-10-02)

We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ...