Annali di Matematica Pura ed Applicata最新文献

We study stable solutions to fractional semilinear equations ((-Delta )^s u = f(u)) in (Omega subset {mathbb {R}}^n), for convex nonlinearities f, and under the Dirichlet exterior condition (u=g) in ({mathbb {R}}^n {setminus } Omega) with general g. We establish a uniqueness and a classification result, and we show that weak (energy) stable solutions can be approximated by a sequence of bounded (and hence regular) stable solutions to similar problems. As an application of our results, we establish the interior regularity of weak (energy) stable solutions to the problem for the half-Laplacian in dimensions (1 leqslant n leqslant 4).

This paper explores the global properties of time-independent systems of operators in the framework of time-periodic Gelfand–Shilov spaces. Our main results provide both necessary and sufficient conditions for global solvability and global hypoellipticity, based on analysis of the symbols of operators. We also present a class of time-dependent operators whose solvability and hypoellipticity are linked to the same properties of an associated time-independent system, albeit with a loss of regularity for temporal variables.

In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical (L^p) spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations.

We derive (C^{1,alpha }) estimates for viscosity solutions of fully nonlinear equations degenerating on a hypersurface.

We study fundamental groups of compact Sasaki manifolds and show that compared to Kähler groups, they exhibit rather different behaviour. This class of groups is not closed under taking direct products, and there is often an upper bound on the dimension of a Sasaki manifold realising a given group. The richest class of Sasaki groups arises in dimension 5.

It is observed that on a compact almost complex Calabi–Yau with torsion 6-manifold the Nijenhuis tensor is parallel with respect to the torsion connection. If the torsion is closed then the space is a compact generalized gradient Ricci soliton. In this case, the torsion connection is Ricci-flat if and only if either the norm of the torsion or the Riemannian scalar curvature is constant. On a compact almost complex Calabi–Yau with torsion 6-manifold it is shown that the curvature of the torsion connection is symmetric on exchange of the first and the second pairs and has vanishing Ricci tensor if and only if it satisfies the Riemannian first Bianchi identity.

Monomial polyhedra are a class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials. In this paper, we completely characterize the (L^p-L^q) boundedness of the Toeplitz operators with radial symbols on monomial polyhedra. This work generalizes the previous results of Toeplitz operators on various generalized Hartogs triangles, as well as extends the recent work of the (L^p) regularity for the Bergman projection on monomial polyhedra.

We study the existence of very weak solutions to a system

with a datum ({pmb {mathsf {mu }}}) being a vector-valued bounded Radon measure and ({{mathcal {A}}}:Omega times {{mathbb {R}}^{ntimes m}}rightarrow {{mathbb {R}}^{ntimes m}}) having measurable dependence on the spacial variable and Orlicz growth with respect to the second variable. We are not restricted to the superquadratic case. For the solutions and their gradients we provide regularity estimates in the generalized Marcinkiewicz scale. In addition, we show a precise sufficient condition for the solution to be a Sobolev function.

Closely related to the pioneering work (Berestycki et al. Commun Pure Appl Math, pp 47–92, 1994) by the authors Berestycki, Nirenberg and Varadhan, we prove maximum and comparison principles for generalized Lane-Emden type systems and as consequences we establish Aleksandrov-Bakelman-Pucci estimates and Harnack-Krylov-Safonov inequalities for related non-homogeneous inequalities, among other results. These contributions go towards a comprehensive understanding on strongly coupled nonlinear elliptic systems.

We present an effective construction of non-Kähler supersymmetric mirror pairs in the sense of Lau, Tseng and Yau (Commun. Math. Phys. 340:145–170, 2015) starting from left-invariant affine structures on Lie groups. Applying this construction we explicitly find SYZ mirror symmetric partners of all known compact 6-dimensional completely solvable solvmanifolds that admit a semi-flat type IIA structure.