Annali di Matematica Pura ed Applicata最新文献

We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature K satisfies

These surfaces are referred to as rotational Ricci surfaces. As an application, we show that there is a one-parameter family of such surfaces meeting the boundary of the unit Euclidean three-ball orthogonally. In addition, we show that this family interpolates a vertical geodesic and the critical catenoid.

We study the analytic and Gevrey regularity for a “sum of squares” operator closely connected to the Schrödinger equation with minimal coupling. We however assume that the (magnetic) vector potential has some degree of homogeneity and that the Hörmander bracket condition is satisfied. It is shown that the local analytic/Gevrey regularity of the solution is related to the multiplicities of the zeroes of the Lie bracket of the vector fields.

We investigate a few aspects of the notion of Levi core, recently introduced by the authors in Dall’Ara, Mongodi (J l’École Polytech Math 10:1047-1095, 2023): a basic finiteness question, the connection with Kohn’s algorithm, and with Catlin’s property (P).

In this paper, we will describe some general properties regarding surfaces with Prym-canonical hyperplane sections, determining also important conditions on the geometric genera of the possible singularities that such a surface can have. Moreover, we will construct new examples of this type of surfaces.

In this article, we investigate some new asymptotic behaviors of the solution for a two-component b-family equations. We first prove the persistence properties of the solution for Eq. (1.1) when the initial data decay logarithmically, algebraically at infinity with the power (beta in (0,infty )). Subsequently, we obtain the infinite propagation of the solution to Eq. (1.1). If the initial data satisfy certain compact condition, then the nontrivial solution u of Eq. (1.1) immediately loses compactly supported. Meanwhile, the solution u decays exponentially as (|x|rightarrow infty ).

Let (Omega ) be a bounded non-smooth domain in (mathbb {R}^n) that satisfies the measure density condition. In this paper, the authors study the interrelations of three basic types of Besov spaces (B_{p,q}^s(Omega )), (mathring{B}_{p,q}^s(Omega )) and (widetilde{B}_{p,q}^s(Omega )) on (Omega ), which are defined, respectively, via the restriction, completion and supporting conditions with (p,qin [1,infty )) and (sin (0,1)). The authors prove that (B_{p,q}^s(Omega )=mathring{B}_{p,q}^s(Omega )=widetilde{B}_{p,q}^s(Omega )), if (Omega ) supports a fractional Besov–Hardy inequality, where the latter is proved under certain conditions on fractional Besov capacity or Aikawa’s dimension of the boundary of (Omega ).

We show that the set of “wild data”, meaning the initial data for which the barotropic Euler system admits infinitely many admissible entropy solutions, is dense in the (L^p)-topology of the phase space.

For large classes of (finite and) infinite dimensional complex Banach spaces Z, B its open unit ball and (f:Brightarrow B) a compact holomorphic fixed-point free map, we introduce and define the Wolff hull, W(f), of f in (partial B) and prove that W(f) is proximal to the images of all subsequential limits of the sequences of iterates ((f^n)_n) of f. The Wolff hull generalises the concept of a Wolff point, where such a point can no longer be uniquely determined, and coincides with the Wolff point if Z is a Hilbert space. Recall that ((f^n)_n) does not generally converge even in finite dimensions, compactness of f (i.e. f(B) is relatively compact) is necessary for convergence in the infinite dimensional Hilbert ball and all accumulation points (Gamma (f)) of ((f^n)_n) map B into (partial B) (for any topology finer than the topology of pointwise convergence on B). The target set of f is

To locate T(f), we use a concept of closed convex holomorphic hull, ({text {Ch}}(x) subset partial B) for each (x in partial B) and define a distinguished Wolff hull W(f). We show that the Wolff hull intersects all hulls from T(f), namely

If B is the Hilbert ball, W(f) is the Wolff point, and this is the usual Denjoy–Wolff result. Our results are for all reflexive Banach spaces having a homogeneous ball (or equivalently, for all finite rank (JB^*)-triples). These include many well-known operator spaces, for example, L(H, K), where either H or K is finite dimensional.

In this paper, we consider the problem of prescribing the (overline{Q}')-curvature on three-dimensional pseudo-Einstein CR manifolds. We study the gradient flow generated by the related functional, and we will prove its convergence to a limit function under suitable assumptions.

We improve the result by Feola and Iandoli (J Math Pures Appl 157:243–281, 2022), showing that quasilinear Hamiltonian Schrödinger type equations are well posed on (H^s({{mathbb {T}}}^d)) if (s>d/2+3). We exploit the sharp paradifferential calculus on ({{mathbb {T}}}^d) developed by Berti et al. (J Dyn Differ Equ 33(3):1475–1513, 2021).