Ricerche di Matematica

Abstract We introduce and investigate the solvable graph $$\Gamma _\mathfrak {S}(L)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Γ</mml:mi> <mml:mi>S</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of a finite-dimensional Lie algebra L over a field F . The vertices are the ele…

Abstract The Squire theorem holds for parallel shear flows governed by the linearized Navier-Stokes equations. In his paper Squire writes “For the study of the stability of flow between parallel walls it is sufficient to confine attention to disturbances of two-dimensional type”, Squire (Proc R Soc A 142:621, 1933). Conversely, for nonlinear Navier-Stokes system it is supposed that the Squire’s t…

Abstract Our aim is to introduce one-sided kinds of the $$\nabla $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∇</mml:mi> </mml:math> –Drazin inverse in associative rings $$\mathcal {R}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> with unity, where $$\begin{aligned} \nabla (\mathcal {R})=\{a\in \mathcal {R}: 1-au \ \mathrm{is \ …

Abstract In the present manuscript we give a structure condition that allows for energy approximation in the vectorial case and we provide two examples, enjoying such a condition.

Abstract In the free, step-2, rank-4 sub-Riemannian Carnot group $$\mathbb {F}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> , we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut locus of the origin $$\operatorname {Cut}(…

Abstract We prove the higher differentiability of integer order of locally bounded minimizers of integral functionals of the form $$\begin{aligned} \mathcal {F}(u,\Omega ):= \,\sum _{i=1}^{n} \dfrac{1}{p_i}\displaystyle \int _\Omega \, a_i(x) |u_{x_i} |^{p_i} dx- \int _\Omega \omega (x)u(x) dx, \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:…