相关论文: Regularity of the nodal set of segregated critical…

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…

We solve the noncommutative Noether's problem for the reflection groups by showing that the skew field of the invariants of the Weyl algebra under the action of any reection group is a Weyl field, that is isomorphic to a skew field of some…

In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type $(P)$ (see below) involving singular nonlinearity and singular weights in smooth…

In this paper we consider nodal radial solutions $u_\epsilon$ to the problem \[ \begin{cases} -\Delta u=\lambda ue^{u^2+|u|^{1+\epsilon}}&\text{ in }B,\\ u=0&\text{ on }\partial B. \end{cases} \] and we study their asymptotic behaviour as…

A reflection principle for Corson compacta holds in the forcing extension obtained by Levy-collapsing a supercompact cardinal to~$\aleph_2$. In this model, a compact Hausdorff space is Corson if and only if all of its continuous images of…

In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists in the complete separability of the Hamilton-Jacobi equations for the…

In the present article a new class $\Upsilon$ of all sets represented in the following form is introduced: $$ \mathbb S_{(s,u)}\equiv\left\{x: x= \Delta^{s}_{{\underbrace{u...u}_{\alpha_1-1}} \alpha_1{\underbrace{u...u}_{\alpha_2…

We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space…

Popov classified crystallographic complex reflection groups by determining lattices they stabilize. These analogs of affine Weyl groups have infinite order and are generated by reflections about affine hyperplanes; most arise as the…

In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensions d $\geq$ 2. Specifically, we consider a microscopic…

We study the Cauchy problem for the two-component Novikov system with initial data $u_0, v_0$ in $H^1(\mathbb{R})$ such that the product $(\partial_x u_0)\partial_x v_0$ belongs to $L^2(\mathbb{R})$. We construct a global semigroup of…

Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z)…

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the "meaningful objects" are the fluxes, evaluated across domain…

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the…

We study the regularity of weak solutions to a certain class of second order parabolic system under the only assumption of continuous coefficients. By using the $A-$caloric approximation argument, we claim that the weak solution $u$ to such…

It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…

This paper is concerned with the location of nodal sets of eigenfunctions of the Dirichlet Laplacian in thin tubular neighbourhoods of hypersurfaces of the Euclidean space of arbitrary dimension. In the limit when the radius of the…

The paper elucidates the relationship between the density of a Banach space and possible sizes of well-separated subsets of its unit sphere. For example, it is proved that for a large enough space $X$, the unit sphere $S_X$ always contains…

We study weakly stable semilinear hyperbolic boundary value problems with highly oscillatory data. Here weak stability means that exponentially growing modes are absent, but the so-called uniform Lopatinskii condition fails at some boundary…

We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, we consider a decomposition $u$ of a bounded Lipschitz set $\Omega\subset\mathbb R^n$ into finitely many subsets of finite perimeter,…