Annali di Matematica Pura ed Applicata最新文献

Let (Omega ) be a bounded, smooth domain of ({mathbb {R}}^{N},) (Nge 2.) For (1<p<N) and (0<q(p)<p^{*}:=frac{Np}{N-p}), let

We prove that if (lim _{prightarrow 1^{+}}q(p)=1,) then (lim _{prightarrow 1^{+}}lambda _{p,q(p)}=h(Omega )), where (h(Omega )) denotes the Cheeger constant of (Omega .) Moreover, we study the behavior of the positive solutions (w_{p,q(p)}) to the Lane–Emden equation (-{text {div}} (left| nabla wright| ^{p-2}nabla w)=left| wright| ^{q-2}w,) as (prightarrow 1^{+}.)

The generalized Zermelo navigation problem looks for the shortest time paths in an environment, modeled by a Finsler manifold (M, F), under the influence of wind or current, represented by a vector field W. The main objective of this paper is to investigate the relationship between the isoparametric functions on the manifold M with and without the presence of the vector field W. Our work generalizes results in (Dong and He in Differ Geom Appl 68:101581, 2020; He et al. in Acta Math Sinica Engl Ser 36:1049–1060, 2020; He et al. in Differ Geom Appl 84:101937, 2022; Ming et al. in Pub Math Debr 97:449–474, 2020; Xu et al. in Isoparametric hypersurfaces induced by navigation in Lorentz Finsler geometry, 2021). For the positive-definite cases, we also compare the mean curvatures in the manifold. Overall, we follow a coordinate-free approach.

In this paper, we derive a nonlinear model for stratified arctic gyres, and prove several results on the existence, uniqueness and stability of solutions to such a model, by assuming suitable conditions for the vorticity function and the density function. The approach consists of deriving a suitable integral formulation for the problem and using fixed-point techniques.

We study varieties (X subseteq {mathbb {P}}^N) of dimension n such that (T_X(k)) is an Ulrich vector bundle for some (k in {mathbb {Z}}). First we give a sharp bound for k in the case of curves. Then we show that (k le n+1) if (2 le n le 12). We classify the pairs ((X,{mathcal {O}}_X(1))) for (k=1) and we show that, for (n ge 4), the case(k=2) does not occur.

The key point to prove the optimal (C^{1,frac{1}{2}}) regularity of the thin obstacle problem is that the frequency at a point of the free boundary (x_0in Gamma (u)), say (N^{x_0}(0^+,u)), satisfies the lower bound (N^{x_0}(0^+,u)ge frac{3}{2}). In this paper, we show an alternative method to prove this estimate, using an epiperimetric inequality for negative energies (W_frac{3}{2}). It allows to say that there are not (lambda -)homogeneous global solutions with (lambda in (1,frac{3}{2})), and by this frequency gap, we obtain the desired lower bound, thus a new self-contained proof of the optimal regularity.

In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively.

We consider the following higher-order prescribed curvature problem on ( {mathbb {S}}^N: )

where (widetilde{K}(y)>0) is a radial function, (m^{*}=frac{2N}{N-2m}), and (D^m) is the 2m-order differential operator given by

where (g=g_{{mathbb {S}}^N}) is the Riemannian metric. We prove the existence of infinitely many double-tower type solutions, which are invariant under some non-trivial sub-groups of O(3), and their energy can be made arbitrarily large.

In this paper we study the following class of linearly coupled systems in the plane:

where (f_{1}, f_{2}) are continuous functions with critical exponential growth in the sense of Trudinger-Moser inequality and (0<lambda <1) is a parameter. First, for any (lambda in (0,1)), by using minimization arguments and minimax estimates we prove the existence of a positive ground state solution. Moreover, we study the asymptotic behavior of these solutions when (lambda rightarrow 0^{+}). This class of systems can model phenomena in nonlinear optics and in plasma physics.

If a Lie group admits a left invariant Randers metric of scalar flag curvature, then it is called of scalar Randers type. In this paper we determine all simply connected three dimensional Lie groups of scalar Randers type. It turns out that such groups must also admit a left invariant Riemannian metric with constant sectional curvature.

Let (nge 2) and (Omega subset mathbb {R}^n) be a bounded Lipschitz domain. Assume that (textbf{b}in L^{n*}(Omega ;mathbb {R}^n)) and (gamma ) is a non-negative function on (partial Omega ) satisfying some mild assumptions, where (n^*:=n) when (nge 3) and (n^*in (2,infty )) when (n=2). In this article, we establish the unique solvability of the Robin problems

and

in the Bessel potential space (L^p_alpha (Omega )), where (alpha in (0,2)) and (pin (1,infty )) satisfy some restraint conditions, and (varvec{nu }) denotes the outward unit normal to the boundary (partial Omega ). The results obtained in this article extend the corresponding results established by Kim and Kwon (Trans Am Math Soc 375:6537–6574, 2022) for the Dirichlet and the Neumann problems to the case of the Robin problem.