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Publisher: Springer-Verlag   (Total: 2329 journals)

 Analysis and Mathematical Physics   [SJR: 0.665]   [H-I: 7]   [4 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1664-2368 - ISSN (Online) 1664-235X    Published by Springer-Verlag  [2329 journals]
• Differential invariants and exact solutions of the Einstein equations
• Authors: Valentin Lychagin; Valeriy Yumaguzhin
Pages: 107 - 115
Abstract: In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.
PubDate: 2017-06-01
DOI: 10.1007/s13324-016-0130-z
Issue No: Vol. 7, No. 2 (2017)

• Radon transforms and Gegenbauer–Chebyshev integrals, I
• Authors: Boris Rubin
Pages: 117 - 150
Abstract: We suggest new modifications of the Helgason’s support theorem and description of the kernel for the hyperplane Radon transform and its dual. The assumptions for functions are formulated in integral terms and close to minimal. The proofs rely on the properties of the Gegenbauer–Chebyshev integrals which generalize Abel type fractional integrals on the positive half-line.
PubDate: 2017-06-01
DOI: 10.1007/s13324-016-0133-9
Issue No: Vol. 7, No. 2 (2017)

• The existence results and Tikhonov regularization method for generalized
mixed variational inequalities in Banach spaces
• Authors: Min Wang
Pages: 151 - 163
Abstract: This paper aims to establish the Tikhonov regularization method for generalized mixed variational inequalities in Banach spaces. For this purpose, we firstly prove a very general existence result for generalized mixed variational inequalities, provided that the mapping involved has the so-called mixed variational inequality property and satisfies a rather weak coercivity condition. Finally, we establish the Tikhonov regularization method for generalized mixed variational inequalities. Our findings extended the results for the generalized variational inequality problem (for short, GVIP(F, K)) in $$R^n$$ spaces (He in Abstr Appl Anal, 2012) to the generalized mixed variational inequality problem (for short, GMVIP $$(F,\phi , K)$$ ) in reflexive Banach spaces. On the other hand, we generalized the corresponding results for the generalized mixed variational inequality problem (for short, GMVIP $$(F,\phi ,K)$$ ) in $$R^n$$ spaces (Fu and He in J Sichuan Norm Univ (Nat Sci) 37:12–17, 2014) to reflexive Banach spaces.
PubDate: 2017-06-01
DOI: 10.1007/s13324-016-0134-8
Issue No: Vol. 7, No. 2 (2017)

• Recovering functions defined on the unit sphere by integration on a
special family of sub-spheres
• Authors: Yehonatan Salman
Pages: 165 - 185
Abstract: The aim of this article is to derive a reconstruction formula for the recovery of $$C^{1}$$ functions, defined on the unit sphere $${{\mathbb {S}}}^{n - 1}$$ , given their integrals on a special family of $$n - 2$$ dimensional sub-spheres. For a fixed point $$\overline{a}$$ strictly inside $${{\mathbb {S}}}^{n - 1}$$ , each sub-sphere in this special family is obtained by intersection of $${{\mathbb {S}}}^{n - 1}$$ with a hyperplane passing through $$\overline{a}$$ . The case $$\overline{a} = 0$$ results in an inversion formula for the special case of integration on great spheres (i.e., Funk transform). The limiting case where $$p\in {{\mathbb {S}}}^{n - 1}$$ and   $$\overline{a}\rightarrow p$$ results in an inversion formula for the special case of integration on spheres passing through a common point in $${{\mathbb {S}}}^{n - 1}$$ .
PubDate: 2017-06-01
DOI: 10.1007/s13324-016-0135-7
Issue No: Vol. 7, No. 2 (2017)

• Boundedness of certain commutators over non-homogeneous metric measure
spaces
• Authors: Haibo Lin; Suqing Wu; Dachun Yang
Pages: 187 - 218
Abstract: Let $$(\mathcal {X},d,\mu )$$ be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let T be a Calderón-Zygmund operator with kernel satisfying only the size condition and some Hörmander-type condition, and $$b\in \widetilde{\mathrm{RBMO}}(\mu )$$ (the regularized BMO space with the discrete coefficient). In this paper, the authors establish the boundedness of the commutator $$T_b:=bT-Tb$$ generated by T and b from the atomic Hardy space $$\widetilde{H}^1(\mu )$$ with the discrete coefficient into the weak Lebesgue space $$L^{1,\,\infty }(\mu )$$ . From this and an interpolation theorem for sublinear operators which is also proved in this paper, the authors further show that the commutator $$T_b$$ is bounded on $$L^p(\mu )$$ for all $$p\in (1,\infty )$$ . Moreover, the boundedness of the commutator generated by the generalized fractional integral $$T_\alpha \,(\alpha \in (0,1))$$ and the $$\widetilde{\mathrm{RBMO}}(\mu )$$ function from $$\widetilde{H}^1(\mu )$$ into $$L^{1/{(1-\alpha )},\,\infty }(\mu )$$ is also presented.
PubDate: 2017-06-01
DOI: 10.1007/s13324-016-0136-6
Issue No: Vol. 7, No. 2 (2017)

• Integrability conditions on a sub-Riemannian structure on $$\mathbb {S}^3$$ S 3
• Authors: Ovidiu Calin; Der-Chen Chang; Jishan Hu
Pages: 9 - 18
Abstract: This paper deals with integrability conditions for a sub-Riemannian system of equations for a step 2 distribution on the sphere $$\mathbb {S}^3$$ . We prove that a certain sub-Riemannian system $$Xf =a$$ , $$Yf =b$$ on $$\mathbb {S}^3$$ has a solution if and only if the following integrability conditions hold: $$X^2 b + 4b = (XY + [X, Y]) a$$ , $$Y^2 a + 4a = (YX-[X, Y]) b$$ . We also provide an explicit construction of the solution f in terms of the vector fields X, Y and functions a and b.
PubDate: 2017-03-01
DOI: 10.1007/s13324-016-0126-8
Issue No: Vol. 7, No. 1 (2017)

• Differential invariants and exact solutions of the Einstein–Maxwell
equation
• Authors: Valentin Lychagin; Valeriy Yumaguzhin
Pages: 19 - 29
Abstract: We construct explicit solutions of the Einstein–Maxwell equations in the case when distributions defined by the Faraday tensor are completely integrable and totally geodesic.
PubDate: 2017-03-01
DOI: 10.1007/s13324-016-0127-7
Issue No: Vol. 7, No. 1 (2017)

• A note for Riesz transforms associated with Schrödinger operators on
the Heisenberg Group
• Authors: Yu Liu; Guobin Tang
Pages: 31 - 45
Abstract: Let $${\mathbb {H}^n}$$ be the Heisenberg group and $$Q=2n+2$$ be its homogeneous dimension. The Schrödinger operator is denoted by $$- {\Delta _{{\mathbb {H}^n}}} + V$$ , where $${\Delta _{{\mathbb {H}^n}}}$$ is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class $${B_{{q_1}}}$$ for $${q_1} \ge \frac{Q}{2}$$ . Let $$H^p_L(\mathbb {H}^n)$$ be the Hardy space associated with the Schrödinger operator for $$\frac{Q}{Q+\delta _0}<p\le 1$$ , where $$\delta _0=\min \{1,2-\frac{Q}{q_1}\}$$ . In this note we show that the operators $${T_1} = V{( - {\Delta _{{\mathbb {H}^n}}} + V)^{ - 1}}$$ and $${T_2} = {V^{1/2}}{( - {\Delta _{{\mathbb {H}^n}}} + V)^{ - 1/2}}$$ are bounded from $$H_L^p({\mathbb {H}^n})$$ into $${L^p}({\mathbb {H}^n})$$ . Our results are also valid on the stratified Lie group.
PubDate: 2017-03-01
DOI: 10.1007/s13324-016-0128-6
Issue No: Vol. 7, No. 1 (2017)

• Entropy solutions for a nonlinear parabolic problems with lower order term
in Orlicz spaces
• Authors: M. Mabdaoui; H. Moussa; M. Rhoudaf
Pages: 47 - 76
Abstract: We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem where A is a Leray–Lions operator having a growth not necessarily of polynomial type. The lower order term $$\Phi$$ : $$\Omega \times (0,T)\times \mathbb {R}\rightarrow \mathbb {R}^N$$ is a Carathéodory function, for a.e. $$(x,t)\in Q_T$$ and for all $$s\in \mathbb {R}$$ , satisfying only a growth condition and the right hand side f belongs to $$L^1(Q_T)$$ .
PubDate: 2017-03-01
DOI: 10.1007/s13324-016-0129-5
Issue No: Vol. 7, No. 1 (2017)

• Matrix Sturm–Liouville equation with a Bessel-type singularity on a
finite interval
• Authors: Natalia Bondarenko
Pages: 77 - 92
Abstract: The matrix Sturm–Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.
PubDate: 2017-03-01
DOI: 10.1007/s13324-016-0131-y
Issue No: Vol. 7, No. 1 (2017)

• Regularity criteria for unsteady MHD third grade fluid due to rotating
porous disk
• Authors: S. Rahman; T. Hayat; B. Ahmad
Pages: 93 - 105
Abstract: The purpose of present paper is to establish the regularity criteria for nonlinear problem of unsteady flow of third grade fluid in a rotating frame. The fluid is between two plates and the lower plate is porous. The main result of this paper is to establish the global regularity of classical solutions when $$\left\ F\right\ _{BMO}^{2}$$ , $$\left\ g\right\ _{BMO}^{2}$$ , $$\left\ \frac{\partial g}{\partial y}\right\ _{BMO}^{2}$$ and $$\left\ \frac{\partial ^{2} g}{\partial y^{2}}\right\ _{BMO}^{2}$$ are sufficiently small. In addition uniqueness of weak solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, F is the velocity and $$g=\nabla \times F=\frac{\partial F}{\partial z}$$ is the vorticity of the rotating fluid.
PubDate: 2017-03-01
DOI: 10.1007/s13324-016-0132-x
Issue No: Vol. 7, No. 1 (2017)

• Hölder continuous solutions to the complex Monge–Ampère equations in
non-smooth pseudoconvex domains
• Authors: Nguyen Xuan Hong; Tran Van Thuy
Abstract: In this paper, we prove the Hölder continuity for solutions to the complex Monge–Ampère equations on non-smooth pseudoconvex domains of plurisubharmonic type m.
PubDate: 2017-05-17
DOI: 10.1007/s13324-017-0175-7

• Unbounded operators in Hilbert space, duality rules, characteristic
projections, and their applications
• Authors: Palle Jorgensen; Erin Pearse; Feng Tian
Abstract: Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces whose intersection contains a fixed vector space $$\mathscr {D}$$ . In the case when $$\mathscr {D}$$ is dense in one of the Hilbert spaces (but not necessarily in the other), we make precise an operator-theoretic linking between the two Hilbert spaces. No relative boundedness is assumed. Nonetheless, under natural assumptions (motivated by potential theory), we prove a theorem where a comparison between the two Hilbert spaces is made via a specific selfadjoint semibounded operator. Applications include physical Hamiltonians, both continuous and discrete (infinite network models), and the operator theory of reflection positivity.
PubDate: 2017-05-17
DOI: 10.1007/s13324-017-0173-9

• Multiplicity of solutions for a class of fractional Choquard–Kirchhoff
equations involving critical nonlinearity
• Authors: Fuliang Wang; Mingqi Xiang
Abstract: The aim of this paper is to investigate the multiplicity of solutions to the following nonlocal fractional Choquard–Kirchhoff type equation involving critical exponent, \begin{aligned}&\left( a+b[u]_{s,p}^p\right) (-\Delta )_p^su=\int _{\mathbb {R}^N}\frac{ u(y) ^{p_{\mu ,s}^*}}{ x-y ^{\mu }}dy u ^{p_{\mu ,s}^*-2}u +\lambda h(x) u ^{q-2}u\quad&\text{ in } \,\,\mathbb {R}^N,\\&[u]_{s,p}=\left( \int _{\mathbb {R}^{N}}\int _{\mathbb {R}^N}\frac{ u(x)- u(y) ^p}{ x-y ^{N+sp}}dxdy\right) ^{1/p} \end{aligned} where $$a\ge 0, b>0$$ , $$0<s<\min \{1,N/2p\}$$ , $$2sp\le \mu <N$$ , $$(-\Delta )_p^s$$ is the fractional p-Laplace operator, $$\lambda >0$$ is a parameter, $$p_{\mu ,s}^*=\frac{(N-\frac{\mu }{2})p}{N-sp}$$ is the critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality, $$1<q<p_s^*=\frac{Np}{N-sp}$$ and $$h\in L^{\frac{p_s^*}{p_s^*-q}}(\mathbb {R}^N)$$ . Under some suitable assumptions, we obtain the multiplicity of nontrivial solutions by using variational methods. In particular, we get the existence of infinitely many nontrivial solutions for the degenerate Kirchhoff case by using Krasnoselskii’s genus theory.
PubDate: 2017-05-06
DOI: 10.1007/s13324-017-0174-8

• A partial inverse problem for the Sturm–Liouville operator on a
star-shaped graph
• Authors: Natalia P. Bondarenko
Abstract: The Sturm–Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from the part of the spectrum. A constructive method is developed for the solution of this problem, based on the Riesz-basicity of some sequence of vector functions. The local solvability of the inverse problem and the stability of its solution are proved.
PubDate: 2017-04-24
DOI: 10.1007/s13324-017-0172-x

• Recovering finite parametric distributions and functions using the
spherical mean transform
• Authors: Yehonatan Salman
Abstract: The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set $$\Gamma$$ . For this, we show how the problem of reconstruction can be converted to a Prony’s type system of equations whose regularity is guaranteed by the assumption that the points in the set $$\Gamma$$ are in general position. By solving the corresponding Prony’s system we can extract the set of parameters which define the corresponding function or distribution.
PubDate: 2017-04-18
DOI: 10.1007/s13324-017-0171-y

• Differential invariants for plane flows of inviscid fluids
• Authors: Anna Duyunova; Valentin Lychagin; Sergey Tychkov
Abstract: Algebras of symmetries and the corresponding algebras of differential invariants for plane flows of inviscid fluids are given. Their dependence on thermodynamical states of media are studied and a classification of thermodynamical states is given.
PubDate: 2017-03-04
DOI: 10.1007/s13324-017-0169-5

• Liouville type theorems of a nonlinear elliptic equation for the V
-Laplacian
• Authors: Guangyue Huang; Zhi Li
Abstract: In this paper, we consider Liouville type theorems for positive solutions to the following nonlinear elliptic equation: \begin{aligned} \Delta _V u+au\log u=0, \end{aligned} where a is a nonzero real constant. By using gradient estimates, we obtain upper bounds of $$\nabla u$$ with respect to $$\sup u$$ and the lower bound of Bakry-Emery Ricci curvature. In particular, for complete noncompact manifolds with $$a<0$$ , we prove that any positive solution must be $$u\equiv 1$$ under a suitable condition for a with respect to the lower bound of Bakry-Emery Ricci curvature. It generalizes a classical result of Yau.
PubDate: 2017-03-01
DOI: 10.1007/s13324-017-0168-6

• Evolution of states in a continuum migration model
• Authors: Yuri Kondratiev; Yuri Kozitsky
Abstract: The Markov evolution of states of a continuum migration model is studied. The model describes an infinite system of entities placed in $${\mathbbm {R}}^d$$ in which the constituents appear (immigrate) with rate b(x) and disappear, also due to competition. For this model, we prove the existence of the evolution of states $$\mu _0 \mapsto \mu _t$$ such that the moments $$\mu _t(N_\Lambda ^n)$$ , $$n\in {\mathbbm {N}}$$ , of the number of entities in compact $$\Lambda \subset {\mathbbm {R}}^d$$ remain bounded for all $$t>0$$ . Under an additional condition, we prove that the density of entities and the second correlation function remain point-wise bounded globally in time.
PubDate: 2017-03-01
DOI: 10.1007/s13324-017-0166-8

• In Memoriam Alexander Vasil’ev (1962–2016)
• PubDate: 2017-01-21
DOI: 10.1007/s13324-016-0160-6

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