Annali di Matematica Pura ed Applicata最新文献

In this paper, we investigate the properties of spreading speeds of the following Fisher-KPP equation in almost periodic media:

where either (mathcal {M}u(t,x)=mathcal {M}^ru(t,x):=partial _x(a(x)partial _{x}u(t,x))+b(x)partial _{x}u(t,x)), which represents the random dispersal, or (mathcal {M}u(t,x)=mathcal {M}^nu(t,x):=int _{mathbb {R}}big (u(t,x-y)-u(t,x)big )dmu (y)), which represents the nonlocal dispersal. With the existence of the spreading speeds (omega ^pm ) in the positive and negative directions of the equation at hand, we 1. give a sufficient and necessary condition for (omega ^+=omega ^-), which means that the propagation of the solution is symmetric when (mathcal {M}=mathcal {M}^r); 2. illustrate that the condition above is a sufficient but not necessary one when (mathcal {M}=mathcal {M}^n); 3. give some other sufficient conditions for (omega ^+=omega ^-) when (mathcal {M}=mathcal {M}^n.)

By using conjugate and disconjugate theorems for second-order linear differential equations, we establish an improvement of the Myers theorem for complete Riemannian manifolds via m-Bakry–Émery Ricci curvature with (varepsilon )-range. In contrast to the classical theorem of S.B. Myers (Duke Math. J. 8:401–404, 1941), our result does not always require non-negativity of the m-Bakry–Émery Ricci curvature in the whole manifold and is new even when the m-Bakry–Émery Ricci curvature is reduced to the Ricci curvature.

We define projective hypersurfaces over finite fields associated to additive polynomials, and show that these are Frobenius superspecial. This means that some powers of the Frobenius endomorphism act on all their étale cohomology groups as scalar multiplication. As an immediate consequence, these hypersurfaces satisfy the semisimplicity conjecture.

In this paper, we would like to study the critical exponent for semi-linear (sigma )-evolution equations with different damping types under the influence of additional regularity for the initial data. On the one hand, we establish the existence of global (in time) solutions for small initial data and the blow-up in finite time solutions in the supercritical case and the subcritical case, respectively. The very interesting phenomenon is that the critical case belonging to the global solution range or the blow-up solution range depends heavily on the assumption of additional regularity for the initial data. Furthermore, we are going to provide lifespan estimates for solutions when the blow-up phenomenon occurs.

The aim of the present paper is to study the orbits of the isotropy group action on an irreducible Hermitian symmetric space of compact type. Specifically, we examine the properties of these orbits as CR submanifolds of a Kähler manifold. Our focus is on the leaves of the totally real distribution, and we investigate the properties of leaves as a Riemannian submanifold. In particular, we prove that any leaf is a totally geodesic submanifold of the orbit. Additionally, we explore the conditions under which each leaf becomes a totally geodesic submanifold of the ambient space. The integrability of the complex distribution is also studied. Moreover, we analyze a contact structure of orbits where the rank of the totally real distribution is 1. We obtain a classification of the orbits that possess either a contact structure or a Sasakian structure compatible with the complex structure on the ambient space. Furthermore, we classify those Sasaki orbits that are Einstein with respect to the induced metric. Specifically, we completely determine Sasaki–Einstein orbits.

We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can be derived that such operators are almost always maximally noncompact in the sense that their ball measure of noncompactness coincides with their operator norm. We point out specifications of the universal principle to the case of the identity operator.

We prove two theorems of Paley and Wiener in the slice regular setting. As an application, we can compute the reproducing kernel for the slice regular Paley–Wiener space, and obtain a related sampling theorem.

We consider the stochastic heat equation which includes a fractional power of the Laplacian of order (alpha in (1, 2]) and it is driven by a nonlinear space-time Gaussian white noise. We study two types of power variations for the solution to this equation: the renormalized quadratic variation and the power variation of order (frac{2alpha }{alpha -1}), both over an equidistant partition of the unit interval. We prove that these two sequences admit nontrivial limits when the mesh of the partition goes to zero. We apply these results to identify certain parameters of the stochastic heat equation.

In this paper, we study an optimization problem of Orlicz mixed volume for multiple convex bodies and prove the existence and uniqueness of the solution. According to the existence and uniqueness of the solution, the concept of Orlicz mixed John ellipsoids is introduced. As an application, we establish the volume ratio inequality. In addition, the connection between the isotropy measure and the characterization of Orlicz mixed John ellipsoids is demonstrated.

We investigate the variational model for nematic elastomers proposed by Barchiesi and DeSimone with the director field defined on the deformed configuration under general growth conditions on the elastic density. This leads us to consider deformations in Orlicz-Sobolev spaces. Our work builds upon a previous paper by Henao and the Second Author, and extends their analysis to the quasistatic setting. The overall strategy parallels the one devised by the First author in the case of Sobolev deformations for a similar model in magnetoelasticity. We prove two existence results for energetic solutions in the rate-independent setting. The first result concerns quasistatic evolutions driven by time-dependent applied loads. For this problem, we establish suitable Poincaré and trace inequalities in modular form to recover the coercivity of the total energy. The second result ensures the existence of quasistatic evolutions for both time-depend applied loads and boundary conditions under physical confinement. In its proof, we follow the approach advanced by Francfort and Mielke based on a multiplicative decomposition of the deformation gradient and we implement it for energies comprising terms defined on the deformed configuration. Both existence results rely on a compactness theorem for sequences of admissible states with uniformly bounded energy which yields the strong convergence of the composition of the nematic fields with the corresponding deformations. While proving it, we show the regular approximate differentiability of Orlicz-Sobolev maps with suitable integrability, thus generalizing a classical result for Sobolev maps due to Goffman and Ziemer.