Mathematische Nachrichten最新文献

We study the existence and Hölder regularity of solutions for fractional evolution equations of order $��\alpha �\in �(�1�,�2�)�$. By means of an analytic resolvent, we construct an interpolation space, which can effectively lower the regularity of initial data. By virtue of the interpolation space and some properties of the analytic resolvent, we derive the existence and Hölder regularity of strict solutions for an inhomogeneous problem, as well as the existence and Hölder regularity of a nonlinear problem.

A two-sided estimate of Lebesgue constants is proposed for the Hölder space $��H_k^{\omega }��\left(�X�\right)��$, constructed from the modulus of continuity of the $�k$th order calculated in the symmetric space $�X$. Choosing different function spaces $�X$, we obtain new criteria for the convergence of classical Fourier series.

In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of $�J$-invariant nilradical and non-$�J$-invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided. In particular, we give a general construction to extend SKT nilpotent Lie algebras to SKT solvable Lie algebras of higher dimension, and we construct new examples of SKT and generalized Kähler compact solvmanifolds.

A smooth ruled surface in 4-space has only parabolic points or inflection points of the real type. We show, by means of contact with transverse planes, that at a parabolic point, there exist two tangent directions determining two planes along which the parallel projection exhibits $�A$-singularities of type butterfly or worse. In particular, such parabolic points can be classified as butterfly hyperbolic, parabolic, or elliptic points depending on the value of the discriminant of a binary differential equation (BDE). Also, whenever such discriminant is positive, we ensure that the integral curves of these directions form a pair of foliations on the ruled surface. Moreover, the set of points that nullify the discriminant is a regular curve transverse to the regular curve formed by inflection points of the real type. Finally, using a particular projective transformation, we obtain a simple parametrization of the ruled surface such that the moduli of its 5-jet identify a butterfly hyperbolic/parabolic/elliptic point, as well as we get the stable configurations of the solutions of BDE in the discriminant curve.

In this paper, we investigate global properties of a class of evolution differential operators defined on a product of tori and spheres. We present a comprehensive characterization of global solvability and hypoellipticity, providing necessary and sufficient conditions that involve Diophantine conditions and the connectedness of sublevel sets associated with the coefficients of the operator. Furthermore, we recover well-known results from existing literature and introduce novel contributions.

We compute the dimension of certain components of the family of smooth determinantal degree $�d$ surfaces in $�P^3$, and show that each of them is the closure of a component of the Noether–Lefschetz locus $��N�L�\left(�d�\right)�$. Our computations exhibit that smooth determinantal surfaces in $�P^3$ of degree 4 form a divisor in $���|��O_{P^3}���\left(�4�\right)��|��$ with five irreducible components. We will compute the degrees of each of these components: $��320�,�2508�,�136512�,�38475�$, and $��320112�$.

Using the Levi-Civita connection on the noncommutative differential 1-forms of a spectral triple $��(�B�,�H�,�D�)�$, we define the full Riemann curvature tensor, the Ricci curvature tensor and scalar curvature. We give a definition of Dirac spectral triples and derive a general Weitzenböck formula for them. We apply these tools to $�\theta$-deformations of compact Riemannian manifolds. We show that the Riemann and Ricci tensors transform naturally under $�\theta$-deformation, whereas the connection Laplacian, Clifford representation of the curvature, and the scalar curvature are all invariant under deformation.

In this paper, we study the twistor space $�Z$ of an oriented Riemannian 4-manifold $�M$ using the moving frame approach, focusing, in particular, on the Einstein, non-self-dual setting. We prove that any general first-order linear condition on the almost complex structures of $�Z$ forces the underlying manifold $�M$ to be self-dual, also recovering most of the known related rigidity results. Thus, we are naturally lead to consider first-order quadratic conditions, showing that the Atiyah–Hitchin–Singer almost Hermitian twistor space of an Einstein 4-manifold bears a resemblance, in a suitable sense, to a nearly Kähler manifold.

In this paper, we study the following Cauchy problem for linear visco-elastic damped wave models with a general time-dependent coefficient $��g�=�g�\left(�t�\right)�$:

This paper is devoted to analyzing the regularity in time and polynomial decay of solutions for a class of fractional reaction–diffusion equations (FrRDEs) involving delays and nonlinear perturbations in a bounded domain of $�R^d$. By establishing some regularity estimates in both time and space variables of the resolvent operator, we present results on the Hölder and $�C^1$-regularity in time of solutions for both time-delayed linear and semilinear FrRDEs. Based on the aforementioned results, we study the existence, uniqueness, and regularity of solutions to an identification problem subjected to the delay FrRDE and the additional observations given at final time. Furthermore, under quite reasonable assumptions on nonlinear perturbations and the technique of measure of noncompactness, the existence of decay solutions with polynomial rates for the problem under consideration is shown.