Conti, Diego Rossi, Federico A.
Published in
Forum Mathematicum

We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for which the nice basis is orthogonal and a more ...

Greenblatt, Michael
Published in
Forum Mathematicum

We extend the theorems of [M. Greenblatt, L p L^{p} Sobolev regularity of averaging operators over hypersurfaces and the Newton polyhedron, J. Funct. Anal. 276 2019, 5, 1510–1527] on L p {L^{p}} to L s p {L^{p}_{s}} Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving L p {L^{p}} t...

Toumi, Mohamed Ali
Published in
Forum Mathematicum

In 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to g...

Sebbar, Abdellah Saber, Hicham
Published in
Forum Mathematicum

This paper concerns the study of the Schwartz differential equation { h , τ } = s E 4 ( τ ) {\{h,\tau\}=s\operatorname{E}_{4}(\tau)} , where E 4 {\operatorname{E}_{4}} is the weight 4 Eisenstein series and s is a complex parameter. In particular, we determine all the values of s for which the solutions h are modular functions for a finite index...

Huo, Zhaohui Jia, Yueling
Published in
Forum Mathematicum

The Cauchy problem of the 2D Zakharov–Kuznetsov equation ∂ t u + ∂ x ( ∂ x x + ∂ y y ) u + u u x = 0 {\partial_{t}u+\partial_{x}(\partial_{xx}+\partial_{yy})u+uu_{x}=0} is considered. It is shown that the 2D Z-K equation is locally well-posed in the endpoint Sobolev space H - 1 / 4 {H^{-1/4}} , and it is globally well-posed in H - 1 / 4...

Byun, Sun-Sig Kim, Wontae Lim, Minkyu
Published in
Forum Mathematicum

We establish a sharp higher integrability near the initial boundary for a weak solution to the following p-Laplacian type system: { u t - div 𝒜 ( x , t , ∇ u ) = div | F | p - 2 F + f in Ω T , u = u 0 on Ω × { 0 } , \left\{\begin{aligned} \displaystyle u_{t}-\operatorname{div}\mathcal{A}(x,t,% \nabla u)&\displaystyle=\operatorname{div}\lv...

Clop, Albert Giova, Raffaella Hatami, Farhad Passarelli di Napoli, Antonia
Published in
Forum Mathematicum

We prove the local Lipschitz continuity and the higher differentiability of local minimizers of functionals of the form 𝔽 ( u , Ω ) = ∫ Ω ( F ( x , D u ( x ) ) + f ( x ) ⋅ u ( x ) ) d x \mathbb{F}(u,\Omega)=\int_{\Omega}(F(x,Du(x))+f(x)\cdot u(x))\mathop{}\!dx with non-autonomous integrand F ( x , ξ ) {F(x,\xi)} which is degenerat...

Naik, Tushar Kanta Nanda, Neha Singh, Mahender
Published in
Forum Mathematicum

The twin group T n {T_{n}} is a right-angled Coxeter group generated by n - 1 {n-1} involutions, and the pure twin group PT n {\mathrm{PT}_{n}} is the kernel of the natural surjection from T n {T_{n}} onto the symmetric group on n symbols. In this paper, we investigate some structural aspects of these groups. We derive a formula for the number of c...

Fechner, Włodzimierz Páles, Zsolt
Published in
Forum Mathematicum

In the present paper, we introduce a new concept of convexity which is generated by a family of endomorphisms of an Abelian group. In Abelian groups, equipped with a translation invariant metric, we define the boundedness, the norm, the modulus of injectivity and the spectral radius of endomorphisms. Beyond the investigation of their properties, ou...

Spirito, Dario
Published in
Forum Mathematicum

We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a na...