Related papers: A notion of $s$-fractional mass for $1$-currents i…

We introduce a class of flat currents with fractal properties, called fractional currents, which satisfy a compactness theorem and remain stable under pushforwards by H\"older continuous maps. In top dimension, fractional currents are the…

This note treats several problems for the fractional perimeter or $s$-perimeter on the sphere. The spherical fractional isoperimetric inequality is established. It turns out that the equality cases are exactly the spherical caps.…

For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in $\R^n$. Moreover, we prove its $\Gamma$-convergence, with respect to the flat topology, and pointwise convergence to the…

In this paper we reconsider the classical nonlinear diffusivity equation of real gas in an heterogenous porous medium in light of the recent studies about the generalized fractional equation of conservation of mass. We first recall the…

Here a new notion of fractional length of a smooth curve, which depends on a parameter $\sigma$, is introduced that is analogous to the fractional perimeter functional of sets that has been studied in recent years. It is shown that in an…

In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…

We prove the $1$-dimensional flat chain conjecture in any complete and quasiconvex metric space, namely that metric $1$-currents can be approximated in mass by normal $1$-currents. The proof relies on a new Banach space isomorphism theorem,…

Since the experimental formation of a vortex with a fractional quantized magnetic flux in a thin superconducting $s$-wave bi-layer was recently reported, we calculate the local density of states (LDOS) around two half quantum vortices in a…

In this paper we establish weak continuity results for the distribution Jacobian minors in fractional sobolev spaces, which can be seen as a extension of recent work of Brezis and Nguyen on the distributional Jacobian determinant. Then we…

We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associated profiles in the small mass limit. We therefore recover a…

We study the soliton modes carrying fractional quantum numbers in one-dimensional superfluids. In the $s$-wave pairing superfluid with the phase of the order parameter twisted by opposite angles $\pm \varphi/2$ at the two ends there is an…

The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a…

Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…

We consider a core-radius approach to nonlocal perimeters governed by isotropic kernels having critical and supercritical exponents, extending the nowadays classical notion of $s$-fractional perimeter, defined for $0<s<1$, to the case $s\ge…

We give a new expression for the supercurrent and its conservation in curved ${\cal N}=1$, $D=4$ superspace using the superconformal approach. The first component of the superfield, whose lowest component is the vector auxiliary field gives…

Here we introduce a fractional notion of $k$-dimensional measure, $0\leq k<n$, that depends on a parameter $\sigma$ that lies between $0$ and $1$. When $k=n-1$ this coincides with the fractional notions of area and perimeter, and when $k=1$…

We prove quasi-invariance of Gaussian measures $\mu_s$ with Cameron-Martin space $H^s$ under the flow of the defocusing nonlinear wave equation with polynomial nonlinearities of any order for all $s>5/2$, including fractional $s$. This…

This paper presents a self-contained new theory of weak fractional differential calculus and fractional Sobolev spaces in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a…

Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M. There is a natural Riemannian metric on the total space B consistent with the metric on M. With respect to that metric, the volume of a rectifiable section…

We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic which provide a…