Acta Mathematica Vietnamica最新文献

This paper is concerned with primal and dual second-order optimality conditions for the second-order strict efficiency of nonsmooth vector equilibrium problem with set, cone and equality conditions. First, we propose some second-order constraint qualifications via the second-order tangent sets. Second, we establish necessary optimality conditions of order two in terms of second-order contingent derivatives and second-order Shi sets for a second-order strict local Pareto minima to such problem under suitable assumptions on the second-order constraint qualifications. An application of the result for the twice Fréchet differentiable functions for the second-order local strict efficiency of that problem is also presented. Some illustrative examples are also provided for our findings.

Endpoint weak-type bounds and non-endpoint strong type bounds are obtained for the spherical maximal function in the setting of Choquet spaces with respect to certain Hausdorff contents or Sobolev capacities.

Partially saturated flow in a porous medium is typically modeled by the Richards equation, which is nonlinear, parabolic and possibly degenerated. This paper presents domain decomposition-based numerical schemes for the Richards equation, in which different time steps can be used in different subdomains. Two global-in-time domain decomposition methods are derived in mixed formulations: the first method is based on the physical transmission conditions and the second method is based on equivalent Robin transmission conditions. For each method, we use substructuring techniques to rewrite the original problem as a nonlinear problem defined on the space-time interfaces between the subdomains. Such a space-time interface problem is linearized using Newton’s method and then solved iteratively by GMRES; each GMRES iteration involves parallel solution of time-dependent problems in the subdomains. Numerical experiments in two dimensions are carried out to verify and compare the convergence and accuracy of the proposed methods with local time stepping.

The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields (L_{m,d}:=mathbb {Q}(zeta _{2^{m}},sqrt {d})), where m ≥ 3 is a positive integer and d is a square-free integer whose prime divisors are congruent to ± 3 (mod 8) or 9 (mod 16).

The corresponding Herz-type Hardy spaces to new weighted Herz spaces (HK^{beta ,p}_{alpha ,q}) associated with the Dunkl operator on (mathbb {R}) have been characterized by atomic decompositions. Later a new characterization of (HK^{beta ,p}_{alpha ,q}) on the real line is introduced. This helped us in the work to characterize that the norms of the Herz-type Hardy spaces for the Dunkl Operator can be achieved by finite central atomic decomposition in some dense subspaces of them. Secondly, as an application we prove that a sublinear operator satisfying many conditions can be uniquely extended to a bounded operator in the Herz-type Hardy spaces for the Dunkl Operator.

Inspired by the definition of balanced neighborly spheres, we define balanced neighborly polynomials and study the existence of these polynomials. The goal of this article is to construct balanced neighborly polynomials of type (k,k,k,k) over any field K for all k≠ 2, and show that a balanced neighborly polynomial of type (2,2,2,2) exists if and only if char(K)≠ 2. Besides, we also discuss a relation between balanced neighborly polynomials and balanced neighborly simplicial spheres.

We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that the quadratic form generated by the Dirichlet-to-Neumann operator controls some sharp homogeneous fractional Sobolev norms. As an application, we prove that the global Lipschitz solutions constructed in Dong et al. (2021) for the one-phase Muskat problem decays exponentially in time in any Hölder norm C^α, α ∈ (0,1).

In this work, we show the existence and multiplicity for the nonlocal Lane-Emden system of the form

where ({varOmega } subset mathbb {R}^{N}) is a C² bounded domain, (mathbb L) is a nonlocal operator, ν,τ are Radon measures on Ω, p,q are positive exponents, and ρ,σ > 0 are positive parameters. Based on a fine analysis of the interaction between the Green kernel associated with (mathbb L), the source terms u^q,v^p and the measure data, we prove the existence of a positive minimal solution. Furthermore, by analyzing the geometry of Palais-Smale sequences in finite dimensional spaces given by the Galerkin type approximations and their appropriate uniform estimates, we establish the existence of a second positive solution, under a smallness condition on the positive parameters ρ,σ and superlinear growth conditions on source terms. The contribution of the paper lies on our unifying technique that is applicable to various types of local and nonlocal operators.

In this paper, we propose two new proximal point methods involving quasi-pseudocontractive mappings in Hadamard spaces. We prove that the first method converges strongly to a common solution of a finite family of minimization problems and fixed point problem for a finite family of quasi-pseudocontractive mappings in an Hadamard space. We then extend this method to a more general method involving multivalued monotone operators to approximate the solution of monotone inclusion problem, which is an important optimization problem. We establish that this method converges strongly to a common zero of a finite family of multivalued monotone operators which is also a common fixed point of a finite family of quasi-pseudocontractive mappings in an Hadamard space. Furthermore, we provide various nontrivial numerical implementations of our method in Hadamard spaces (which are non-Hilbert) and compare them with some other recent methods in the literature.